19A-B. Calculus for Science, Engineering, and Mathematics.

Catalog copy
Ma19A: The limit of a function, calculating limits, continuity,
 tangents, velocities, and other instantaneous rates of
 change. Derivatives, the chain rule, implicit differentiation, higher
 derivatives. Exponential functions, inverse functions, and their
 derivatives. The mean value theorem, monotonic functions, concavity,
 and points of inflection.  Applied maximum and minimum
 problems. Students cannot receive credit for this course and course
 11A and Economics 11A.  
Ma19B: The definite integral and the fundamental theorem of calculus.
 Areas, volumes. Integration by parts, trigonometric substitution, and
 partial fractions methods. Improper integrals. Sequences, series,
 absolute convergence and convergence tests. Power series, Taylor and
 Maclaurin series.  Students may not receive credit for both this
 course and course 11B.

Prerequisite(s):
19A: Math 2B or 3 or Engineering 3 or Math placement exam (40 or higher)
  placement exam;
19B: Math 19A.
 (General Education Codes: IN, Q.)

Explanation of prerequisites:
MA 19AB comprise the standard single-variable calculus sequence at UCSC;
 they require a pre-calculus mathematical background, as given either by
 pre-university education or by the pre-calculus class Math 3/Engineering 3.

Required Skills to pass course 19A:
1. The understanding of concepts of a function, its limits, derivatives
   and inverse.
2. The ability to use the chain rule and to perform implicit differentiation.
3. The ability to find the extremal points of a function and classify them
   as maxima, minima or points of inflexion.

Required Skills to pass course 19B:
1. The understanding of the fundamental theorem of calculus, and the
   notion of definite, indefinite and improper integrals.
2. The ability to integrate a wide class of functions using the
   techniques of integration-by-parts, substitution and partial fractions.
3. An elementary knowledge of the properties of sequences and series.

Core topics (must be taught): 19A
1. Definition of a function, its limits, continuity and derivative.
2. The chain rule and implicit differentiation.
3. The inverse of a function.
4. The Mean Value Theorem.
5. The monotonicity of a function and concavity.
6. Extremal points of a function.

Core topics (must be taught): 19B
1. The definite integral and the fundamental theorem of calculus.
2. Areas and volumes.
3. Integration techniques: integration by parts, substitution and partial
   fractions.
4. Improper integrals.
5. Sequences and series (convergence, power series, Talyor series).


Optional topics, 19A:
1. Applications from differential equations, geometry, probability
   and physics.

Optional topics, 19B:
1. Applications from differential equations, geometry, probability
   and physics.


Text
"Calculus Early Transcendentals", J. Stewart, fourth edition.

Prepared by Neil Balmforth, 9/02