UCLA | Department of Bioengineering

1. Bioengineering 10; Chemistry and Biochemistry 20A, 20B, 20L, 30A, 30AL, 30B, 30BL; Computer Science 31; Life Sciences 2 (satisfies HSSSEAS GE life sciences requirement), 3, 4; Mathematics 31A, 31B, 32A, 32B, 33A, 33B; Physics 1A, 1B, 1C, 4AL, 4BL.

The Major

1. Bioengineering 100, 110, 120, 165, 176, 180, 180L, 181,181L, 182A, 182B, 182C;
Chemistry & Biochemistry 153A

2. Three breadth course (12 units) selected from an approved list available in the Office of Academic and Student Affairs or see Undergraduate Technical Breath Areas at http://www.seasoasa.ucla.edu/

3. Any two elective courses from: Bioengineering, M105, M106, M131, M172; Biomedical Engineering C101, CM102, CM103, CM145, M150, M150L, C170, C171, CM180, C181, CM183, C185, C187

For information on University and general education requirements, see Requirements for B.S. Degrees on pages 21-22 of the HSSEAS Announcement for details or http://www.registrar.ucla.edu/ge/GE-EngrNew07-08.pdf

Bioengineering (top of page)

10. Introduction to Bioengineering. (2)

Lecture, two hours; outside study, fours hours. Requisite: High School level physics, chemistry, biology and mathematics, or consent of instructor. Introduction to the scientific and technological bases for the established and emerging sub-fields of bioengineering including biosensors, bioinstrumentation and biosignal processing, biomechanics, biomaterials, tissue engineering, biotechnology, biological imaging, biomedical optics and lasers, neuroengineering, protein and cell engineering, and biomolecular machines. Letter grading.

19. Fiat Lux Freshman Seminars. (1)

Seminar, one hour. Discussion of and critical thinking about topics of current intellectual importance, taught by faculty members in their areas of expertise and illuminating many paths of discovery at UCLA. P/NP grading.

100. Bioengineering Fundamentals (4)

Lecture, four hours; discussion, one hour; outside study, seven hours. Requisites or corequisites: Electrical Engineering 1 or Physics 1C, and Mathematics 32B. Fundamental basis for analysis and design of biological and biomedical devices and systems. Classical and statistical thermodynamic analysis of biological systems. Material, energy, charge, and force balances. Introduction to network analysis. Letter grading.

M105. Biopolymer Chemistry and Bioconjugates (4)

(Same as Biomedical Engineering CM105.) Lecture, four hours; discussion, one hour; outside study, seven hours. Enforced requisites: Chemistry 20A, 20B, 20L. Highly recommended: one organic chemistry course. Bioconjugate chemistry is science of coupling biomolecules for wide range of applications. Oligonucleotides may be coupled to one surface in gene chip, or one protein may be coupled to one polymer to enhance its stability in serum. Wide variety of bioconjugates are used in delivery of pharmaceuticals, in sensors, in medial diagnostics, and in tissue engineering. Basic concepts of chemical ligation, including choice and design of conjugate linkers depending on type of biomolecule and desired application, such as degradable versus nondegradable linkers. Presentation and discussion of design and synthesis of synthetic bioconjugates for some sample applications. Letter grading.

M106. Topics in Biophysics, Channels, and Membranes (4)

(Same as Biomedical Engineering CM106.) Lecture, three hours; discussion, one hour; outside study, eight hours. Requisites: Chemistry 14C, Life Sciences 1, 2, 3, 4, Mathematics 33B, Physics 1C, 4AL, 4BL. Coverage in depth of physical processes associated with biological membranes and channel proteins, with specific emphasis on electrophysiology. Basic physical principles governing electrostatics in dielectric media, building on complexity to ultimately address action potentials and signal propagation in nerves. Topics include Nernst/Planck and Poisson/Boltzmann equations, Nernst potential, Donnan equilibrium, GHK equations, energy barriers in ion channels, cable equation, action potentials, Hodgkin/Huxley equations, impulse propagation, axon geometry and conduction, dendritic integration. Letter grading.

110. Biotransport and Reaction Processes (4)

Lecture, four hours; discussion, one hour; outside study, seven hours. Requisites: course 100, Computer Science 31 or Mechanical and Aerospace Engineering 20, Mathematics 33B. Introduction to analysis of fluid flow, heat transfer, mass transfer, binding events, and biochemical reactions in systems of interest to bioengineers, including cells, tissues, organs, human body, extracorporeal devices, tissue engineering systems, and bioartificial organs. Introduction to pharmacokinetic analysis. Letter grading.

120. Biomedical Transducers (4)

Lecture, four hours; discussion, one hour; outside study, seven hours. Requisites: Chemistry 14C or 30A, Electrical Engineering 1 or Physics 1C, Mathematics 32B. Principles of transduction, design characteristics for different measurements, reliability and performance characteristics, and data processing and recording. Emphasis on silicon-based microfabricated and nanofabricated sensors. Novel materials, biocompatibility, biostability. Safety of electronic interfaces. Actuator design and interfacing control. Letter grading.

M131. Nanopore Sensing (4)

(Same as Biomedical Engineering CM131.) Lecture, four hours; discussion, one hour; outside study, seven hours. Requisites: courses 100, 120, Life Sciences 2, 3, Physics 1A, 1B, 1C. Analysis of sensors based on measurements of fluctuating ionic conductance through artificial or protein nanopores. Physics of pore conductance. Applications to single molecule detection and DNA sequencing. Review of current literature and technological applications. History and instrumentation of resistive pulse sensing, theory and instrumentation of electrical measurements in electrolytes, nanopore fabrication, ionic conductance through pores and GHK equation, patch clamp and single channel measurements and instrumentation, noise issues, protein engineering, molecular sensing, DNA sequencing, membrane engineering, and future directions of field. Letter grading.

165. Bioethics and Regulatory Policies in Bioengineering. (4)

Lecture, four hours; discussion, one hour, outside study, seven hours. Requisite: Bioengr 180. The increasing pace of biotechnological development requires an intensive preparation for young scientists on the issues in bioethics and regulatory policy. Students will examine the role of scientists in participating, supporting or opposing the establishment of regulatory frameworks, will understand the relationship between scientists and socioeconomic movements by the general public and individuals, and will discuss the role of scientists in public arena, academic institutions, media and industry. This course may be appropriate for those who already have some knowledge and/or experience in molecular biology, genetics, or biotechnology. Letter grading.

M172 . Design of Minimally Invasive Surgical Tools. (4)

(Same as Biomedical Engineering CM172.) Lecture, three hours; discussion, two hours; outside study, seven hours. Requisites: Chemistry 30B, Life Sciences 2, 3, Mathematics 32A. Introduction to design principles and engineering concepts used in design and manufacture of tools for minimally invasive surgery. Coverage of FDA regulatory policy and surgical procedures. Topics include optical devices, endoscopes and laparoscopes, biopsy devices, laparoscopic tools, cardiovascular and interventional radiology devices, orthopedic instrumentation, and integration of devices with therapy. Examination of complex process of tool design, fabrication, testing, and validation. Preparation of drawings and consideration of development of new and novel devices. Letter grading.

176. Principles of Biocompatibility. (4)

Lecture, four hours; discussion, two hours; outside study, six hours. Requisites: Chemistry 153A, Electrical Engineering 1 or Physics 1C, Mathematics 33B. Biocompatibility at systemic, tissue, cellular, and molecular levels. Biomechanical compatibility, stress/strain constitutive equations, cellular and molecular response to mechanical signals, biochemical and cellular compatibility, immune response. Letter grading.

180. Systems Integration in Biology, Engineering, and Medicine I (SIBEM I). (4)

Lecture, three hours; discussion, two hours; outside study, seven hours. Requisites: courses 100, 110, 120, Life Sciences 3, Physics 4BL. Corequisite: course 180L. Part I of two-part series. Molecular basis of normal physiology and pathophysiology, and engineering design principles of cardiovascular and pulmonary systems. Fundamental engineering principles of selected medical therapeutic devices. Letter grading.

180L. Systems Integration in Biology, Engineering, and Medicine II Laboratory (SIBEM I Laboratory). (3)

Lecture, one hour; laboratory, four hours; clinical visits, three hours; outside study, one hour. Corequisite: course 180. Hands-on experimentation and clinical applications of selected medical therapeutic devices associated with cardiovascular and pulmonary disorders. Letter grading.

181. Systems Integration in Biology, Engineering, and Medicine II (SIBEM II). (4)

Lecture, three hours; discussion, two hours; outside study, seven hours. Requisite: course 180L. Corequisite: course 181L. Part II of two-part series. Molecular basis of normal physiology and pathophysiology of selected organ systems; engineering design principles of digestive and urinary systems. Fundamental engineering principles of selected medical therapeutic devices. Letter grading.

181L. Systems Integration in Biology, Engineering, and Medicine II Laboratory (SIBEM II Laboratory). (3)

Lecture, one hour; laboratory, four hours; clinical visits, three hours; outside study, one hour. Corequisite: course 181. Hands-on experimentation and clinical applications of molecular basis of normal physiology and pathophysiology of selected organ systems; engineering design principles of digestive and urinary systems. Letter grading.

182A. Bioengineering Capstone Design I. (4)

Lecture, two hours; laboratory, six hours; outside study, four hours. Requisites: course 120, Physics 4BL. Lectures, design seminars, and discussions with faculty advisory panel. Working in teams, students compete to develop innovative bioengineering solutions to meet specific set of design criteria (design and make strongest self-assembled biorobots or most stable UCLA logo or most selective and efficient biomarker sensors, etc.). Development, writing, and oral defense of student design proposals. Letter grading.

182B. Bioengineering Capstone Design II. (4)

Lecture, two hours; laboratory, six hours; outside study, four hours. Requisite: course 182A. Lectures, design seminars, and discussions with faculty advisory panel. Working in teams, students compete to develop innovative bioengineering solutions to meet specific set of design criteria (design and make strongest self-assembled biorobots or most stable UCLA logo or most selective and efficient biomarker sensors, etc.). Exploration of different experimental and computational methods. Ordering of specific materials and software that are relevant to student projects. Letter grading.

182C. Bioengineering Capstone Design III. (4)

Lecture, two hours; laboratory, six hours; outside study, four hours. Requisite: course 182B. Lectures, design seminars, and discussions with faculty advisory panel. Working in teams, students compete to develop innovative bioengineering solutions to meet specific set of design criteria (design and make strongest self-assembled biorobots or most stable UCLA logo or most selective and efficient biomarker sensors, etc.). Construction of student designs, project updates, presentation of final projects in written and oral format, and team competition. Letter grading.

M183. Targeted Drug Delivery and Controlled Drug Release. (4)

(Same as Biomedical Engineering CM183.) Lecture, three hours; discussion, two hours; outside study, seven hours. Requisites: Chemistry 20A, 20B, 20L. New therapeutics require comprehensive understanding of modern biology, physiology, biomaterials, and engineering. Targeted delivery of genes and drugs and their controlled release are important in treatment of challenging diseases and relevant to tissue engineering and regenerative medicine. Drug pharmacodynamics and clinical pharmacokinetics. Application of engineering principles (diffusion, transport, kinetics) to problems in drug formulation and delivery to establish rationale for design and development of novel drug delivery systems that can provide spatial and temporal control of drug release. Introduction to biomaterials with specialized structural and interfacial properties. Exploration of both chemistry of materials and physical presentation of devices and compounds used in delivery and release. Letter grading.

Biomedical Engineering (top of page)

C101. Introduction to Biomedical Engineering. (4)

(Formerly numbered 101.) Lecture, four hours; laboratory, three hours; outside study, five hours. Designed for physical sciences, life sciences, and engineering students. Instead of presenting a general overview of biomedical engineering, this course provides an in-depth, quantitative analysis of a few topics in biomedical engineering. Concurrently scheduled with course C201. Letter grading.

CM102. Basic Human Biology for Biomedical Engineers I. (4)

(Formerly numbered M102.) (Same as Physiological Science CM102.) Lecture, three hours; laboratory, two hours. Preparation: human molecular biology, biochemistry, and cell biology. Not open for credit to Physiological Science majors. Molecular-level understanding of human physiology in selected organ systems. Analysis of the functional basis of biomedical instrumentation. Actual demonstration of biomedical instruments, as well as visits to biomedical facilities. Concurrently scheduled with course CM202. Letter grading.

CM103. Basic Human Biology for Biomedical Engineers II. (4)

(Formerly numbered M103.) (Same as Physiological Science CM103.) Lecture, three hours; laboratory, two hours. Preparation: human molecular biology, biochemistry, and cell biology. Not open for credit to Physiological Science majors. Molecular-level understanding of human physiology in selected organ systems. Analysis of the functional basis of biomedical instrumentation. Actual demonstration of biomedical instruments, as well as visits to biomedical facilities. Concurrently scheduled with course CM203. Letter grading.

CM131. Nanopore Sensing (4)

(Same as Bioengineering M131.) Lecture, four hours; discussion, one hour; outside study, seven hours. Requisites: Bioengineering 100, 120, Life Sciences 2, 3, Physics 1A, 1B, 1C. Analysis of sensors based on measurements of fluctuating ionic conductance through artificial or protein nanopores. Physics of pore conductance. Applications to single molecule detection and DNA sequencing. Review of current literature and technological applications. History and instrumentation of resistive pulse sensing, theory and instrumentation of electrical measurements in electrolytes, nanopore fabrication, ionic conductance through pores and GHK equation, patch clamp and single channel measurements and instrumentation, noise issues, protein engineering, molecular sensing, DNA sequencing, membrane engineering, and future directions of field. Concurrently scheduled with course C231. Letter grading.

CM145. Molecular Biotechnology for Engineers. (4)

(Same as Chemical Engineering CM145.) Lecture, four hours; outside study, eight hours. Selected topics in molecular biology that form the foundation of biotechnology and the biomedical industry today. Topics include recombinant DNA technology, molecular research tools, manipulation of gene expression, directed mutagenesis and protein engineering, DNA-based diagnostics and DNA microarrays, antibody and protein-based diagnostics, genomics and bioinformatics, isolation of human genes, gene therapy, and tissue engineering. Concurrently scheduled with course CM245. Letter grading.

M150L. Introduction to Micromachining and Microelectromechanical Systems Laboratory. (4)

(Same as Electrical Engineering M150L and Mechanical and Aerospace Engineering M180L.) Lecture, three hours; laboratory, four hours; outside study, five hours. Requisites: Electrical Engineering 1 or Physics 1C, Chemistry 20A. Introduction to micromachining technologies and microelectromechanical systems (MEMS). Methods of micromachining and how these methods can be used to produce a variety of MEMS, including microstructures, microsensors, and microactuators. Students fabricate set of basic MEMS structures in hands-on microfabrication laboratory. Letter grading.

C170. Laser-Tissue Interaction I. (4)

Lecture, three hours; laboratory, three hours; outside study, six hours. Requisites: Electrical Engineering 172, 175, Life Sciences 3, Physics 17. Introduction to different types of laser-tissue interaction, with emphasis on therapeutics and diagnostics applications. Concurrently scheduled with course C270. Letter grading.

C171. Laser-Tissue Interaction II: Biological Spectroscopy. (4)

Lecture, four hours; outside study, eight hours. Requisite: course C170. Designed for physical sciences, life sciences, and engineering majors. Introduction to optical spectroscopy principles, design of spectroscopic measurement devices, optical properties of tissues, and fluorescence spectroscopy of biological media. Concurrently scheduled with course C271. Letter grading.

CM172 . Design of Minimally Invasive Surgical Tools. (4)

(Same as Bioengineering M172.) Lecture, three hours; discussion, two hours; outside study, seven hours. Requisites: Chemistry 30B, Life Sciences 2, 3, Mathematics 32A. Introduction to design principles and engineering concepts used in design and manufacture of tools for minimally invasive surgery. Coverage of FDA regulatory policy and surgical procedures. Topics include optical devices, endoscopes and laparoscopes, biopsy devices, laparoscopic tools, cardiovascular and interventional radiology devices, orthopedic instrumentation, and integration of devices with therapy. Examination of complex process of tool design, fabrication, testing, and validation. Preparation of drawings and consideration of development of new and novel devices. Concurrently scheduled with course C272. Letter grading.

CM180. Introduction to Biomaterials. (4)

(Formerly numbered M180.) (Same as Materials Science CM180.) Lecture, three hours; outside study, nine hours. Requisites: Chemistry 20A, 20B, and 20L, or Materials Science 14. Engineering materials used in medicine and dentistry for repair and/or restoration of damaged natural tissues. Topics include relationships between material properties, suitability to task, surface chemistry, processing and treatment methods, and biocompatibility. Concurrently scheduled with course CM280. Letter grading.

C181. Biomaterials-Tissue Interactions (4)

Lecture, 3 hours. Requisites: Biomed CM180 or consent of instructor. In-depth exploration of host cellular response to biomaterials; vascular response, interface and clotting, biocompatibility, animal models, inflammation, infection, extracellular matrix, cell adhesion, and role of mechanical forces. Letter grading.

CM183. Targeted Drug Delivery and Controlled Drug Release. (4)

(Same as Bioengineering M183.) Lecture, three hours; discussion, two hours; outside study, seven hours. Requisites: Chemistry 20A, 20B, 20L. New therapeutics require comprehensive understanding of modern biology, physiology, biomaterials, and engineering. Targeted delivery of genes and drugs and their controlled release are important in treatment of challenging diseases and relevant to tissue engineering and regenerative medicine. Drug pharmacodynamics and clinical pharmacokinetics. Application of engineering principles (diffusion, transport, kinetics) to problems in drug formulation and delivery to establish rationale for design and development of novel drug delivery systems that can provide spatial and temporal control of drug release. Introduction to biomaterials with specialized structural and interfacial properties. Exploration of both chemistry of materials and physical presentation of devices and compounds used in delivery and release. Concurrently scheduled with course C283. Letter grading.

C185. Introduction to Tissue Engineering. (4)

Lecture, three hours; outside study, nine hours. Requisites: course CM102 or CM202, Chemistry 20A, 20B, 20L. Tissue engineering applies principles of biology and physical sciences with an engineering approach to regenerate tissues and organs. Guiding principles for proper selection of three basic components for tissue engineering: cells, scaffolds, and molecular signals. Concurrently scheduled with course C285. Letter grading.

C187. Applied Tissue Engineering. (4)

Lecture, three hours; discussion, two hours; outside study, seven hours. Requisites: course CM102, Chemistry 20A, 20B, 20L, Life Sciences 1 or 2. Overview of central topics of tissue engineering, with focus on how to build artificial tissues into regulated clinically viable products. Topics include biomaterials selection, cell source, delivery methods, FDA approval processes, and physical/chemical and biological testing. Case studies include skin and artificial skin, bone and cartilage, blood vessels, neurotissue engineering, and liver, kidney, and other organs. Clinical and industrial perspectives of tissue engineering products. Manufacturing constraints, clinical limitations, and regulatory challenges in design and development of tissue-engineering devices. Concurrently scheduled with course C287. Letter grading.

Chemistry and Biochemistry (top of page)

20A. Chemical Structures. (4)

Lecture, three hours; discussion, one hour. Preparation: high school chemistry or equivalent background and three and one-half years of high school mathematics. Recommended: high school physics. Enforced requisite: successful completion of Chemistry Diagnostic Examination. First term of general chemistry. Survey of chemical processes, quantum chemistry, atomic and molecular structure and bonding, molecular spectroscopy. P/NP or letter grading.

20B. Chemical Energetics and Change. (4)

Lecture, three hours; discussion, one hour. Enforced requisites: course 20A or 20AH, and Mathematics 31A, with grades of C- or better. Second term of general chemistry. Intermolecular forces and organization, phase behavior, chemical thermodynamics, solutions, equilibria, reaction rates and laws. P/NP or letter grading.

20L. General Chemistry Laboratory I. (3)

Lecture, one hour; laboratory, three hours. Enforced requisite: course 20A with a grade of C- or better. Enforced corequisite: course 20B. Use of the balance, volumetric techniques, volumetric and potentiometric analysis; Beer's law, applications for environmental analysis and materials science. P/NP or letter grading.

30A. Chemical Dynamics and Reactivity: Introduction to Organic Chemistry. (4)

Lecture, three hours; discussion, one hour. Enforced requisite: course 20B with a grade of C- or better. First term of organic chemistry. Mechanisms of organic and inorganic reactions, including redox, elimination, addition, substitution, and radical processes. P/NP or letter grading.

30AL. General Chemistry Laboratory II. (4)

Lecture, one hour; laboratory, six hours. Enforced requisites: courses 20B (or 20BH) and 20L, with grades of C- or better. Enforced corequisite: course 30A or 30AH. Qualitative and quantitative analysis of chemical reactions and compounds, kinetics, separations, and spectroscopy. P/NP or letter grading.

30B. Organic Chemistry: Reactivity and Synthesis, Part I. (4)

Lecture, three hours; discussion, one hour. Enforced requisite: course 30A or 30AH, with a grade of C- or better. Second term of organic chemistry. Synthesis, properties, and reactions of organic functional groups, including alcohols, alkenes, alkynes, aromatic compounds, aldehydes, ketones, carboxyl derivatives, and amines. P/NP or letter grading.

30BL. Organic Chemistry Laboratory I. (3)

Lecture, one hour; laboratory, four hours. Enforced requisites: courses 30A (or 30AH) and 30AL, with grades of C- or better. Enforced corequisite: course 30B. Basic experimental techniques in organic synthesis (distillation, extraction, crystallization, and performing reactions) and organic analytical chemistry (melting and boiling point, refractive index, chromatography, IR, NMR, GC). Single and multistep synthesis of known organic molecules on microscale level. P/NP or letter grading.

153A. Biochemistry: Introduction to Structure, Enzymes, and Metabolism. (4)

Lecture, four hours; discussion, one hour. Requisite: course 14D or 30B with a grade of C- or better. Recommended: Life Sciences 2, 3. Structure of proteins, carbohydrates, and lipids; enzyme catalysis and principles of metabolism, including glycolysis, citric acid cycle, and oxidative phosphorylation. Letter grading.

Computer Science (top of page)

31. Introduction to Computer Science I. (4)

Lecture, four hours; discussion, two hours; outside study, six hours. Limited to Computer Science and Electrical Engineering majors. Introduction to computer science via theory, applications, and programming. Basic data types, operators and control structures. Input/output. Procedural and data abstraction. Introduction to object-oriented software development. Functions, recursion. Arrays, strings, pointers. Abstract data types, object-oriented programming. Examples and exercises from computer science theory and applications. Letter grading.

English (top of page)

3. English Composition, Rhetoric, and Language. (5)

Lecture, three hours. Enforced requisites: satisfaction of Subject A requirement, course 2 or English as a Second Language 35 (C or better). Rhetorical techniques and skillful argument. Analysis of varieties of academic prose and writing of a minimum of 20 pages of revised text. Completion of course with a grade of C or better satisfies Letters and Science Writing I requirement. Letter grading.

Life Science (top of page)

2. Cells, Tissues, and Organs. (5)

Lecture, three hours; discussion/laboratory, three hours (alternate weeks). Enforced requisite: Chemistry 14A or 20A. Not open for credit to students with credit for course 2W. Introduction to basic principles of cell structure, organization of cells into tissues and organs, and principles of organ systems. Letter grading.

3. Introduction to Molecular Biology. (5)

Lecture, three hours; discussion/laboratory, three hours (alternate weeks). Enforced requisites: course 2 or 2W, Chemistry 14C or 30A or former course 10D or 30. Introduction to basic principles of biochemistry and molecular biology. Letter grading.

4. Genetics. (5)

Lecture, three hours; discussion, two hours. Enforced requisite: course 3. Principles of Mendelian inheritance and chromosomal basis of heredity in prokaryotes and eukaryotes, recombination, biochemical genetics, mutation, DNA, genetic code, gene regulation, genes in populations. Letter grading.

Mathematics (top of page)

31A. Differential Calculus. (4)

Lecture, three hours; discussion, one hour. Preparation: at least three and one-half years of high school mathematics (including some coordinate geometry and trigonometry). Requisite: successful completion of Mathematics Diagnostic Test or course 1 with a grade of C- or better. Differential calculus and applications; introduction to integration. P/NP or letter grading.

31B. Integration and Infinite Series. (4)

Lecture, three hours; discussion, one hour. Requisite: course 31A with a grade of C- or better. Transcendental functions; methods and applications of integration; sequences and series. P/NP or letter grading.

32A. Calculus of Several Variables. (4)

Lecture, three hours; discussion, one hour. Requisite: course 31B with a grade of C- or better. Introduction to differential calculus of several variables, vector field theory. P/NP or letter grading.

32B. Calculus of Several Variables. (4)

Lecture, three hours; discussion, one hour. Requisite: course 32A with a grade of C- or better. Introduction to integral calculus of several variables, line and surface integrals. P/NP or letter grading.

33A. Linear Algebra and Applications. (4)

Lecture, three hours; discussion, one hour. Requisite: course 32A with a grade of C- or better. Introduction to linear algebra: systems of linear equations, matrix algebra, linear independence, subspaces, bases and dimension, orthogonality, least-squares methods, determinants, eigenvalues and eigenvectors, matrix diagonalization, and symmetric matrices. P/NP or letter grading.

33B. Differential Equations. (4)

Lecture, three hours; discussion, one hour. Requisite: course 32A with a grade of C- or better. Highly recommended: course 33A. First-order, linear differential equations; second-order, linear differential equations with constant coefficients; power series solutions; linear systems. P/NP or letter grading.

Physics (top of page)

1A. Physics for Scientists and Engineers: Mechanics. (5)

Lecture/demonstration, four hours; discussion, one hour. Recommended preparation: high school physics, one year of high school calculus or Mathematics 31A and 31B. Enforced requisite: Mathematics 31A. Enforced corequisite: Mathematics 31B. Recommended corequisite: Mathematics 32A. Motion, Newton laws, work, energy, linear and angular momentum, rotation, equilibrium, gravitation. P/NP or letter grading.

1B. Physics for Scientists and Engineers: Oscillations, Waves, Electric and Magnetic Fields. (5)

Lecture/demonstration, four hours; discussion, one hour. Enforced requisites: course 1A, Mathematics 31B. Enforced corequisite: Mathematics 32A. Recommended corequisite: Mathematics 32B. Damped and driven oscillators, mechanical and acoustic waves. Electrostatics: electric field and potential, capacitors, and dielectrics. Currents and DC circuits. Magnetic field. P/NP or letter grading.

1C. Physics for Scientists and Engineers: Electrodynamics, Optics, and Special Relativity. (5)

Lecture/demonstration, four hours; discussion, one hour. Enforced requisites: courses 1A, 1B, Mathematics 32A. Enforced corequisite: Mathematics 32B. Recommended corequisite: Mathematics 33A. Ampere law, Faraday law, inductance, and LRC circuits. Maxwell equations in integral and differential form. Electromagnetic waves. Light, geometrical, and physical optics. Special relativity. P/NP or letter grading.

4AL. Physics Laboratory for Scientists and Engineers: Mechanics (2)

Laboratory, three hours. Enforced requisite: course 1A or 1AH. Enforced corequisite: course 1B or 1BH. Experiments on measuring gravity, accelerated motion, kinetic and potential energy, impulse and momentum, damped and driven oscillators, resonance and vibrating strings. Computer data acquisition and analysis. Introduction to error analysis, including distributions and least-squares fitting procedures. Letter grading.

4BL. Physics Laboratory for Scientists and Engineers: Electricity and Magnetism(2)

Laboratory, three hours. Enforced requisite: course 1A or 1AH. Enforced corequisite: course 1B or 1BH. Experiments on electric forces, fields, and potentials. Magnetic fields. Linear and nonlinear devices. Resistors, capacitors, and inductors. Modern circuits. Geometrical and physical optics. Letter grading.


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