Brief Calculus
 Course: MAT213 First Term: 2018 Fall Final Term: Current Final Term: 2020 Spring Lecture   4.0 Credit(s)   4.0 Period(s)   4.0 Load       Credit(s)    Period(s)    Load Subject Type: Academic Load Formula: S

Description: Introduction to the theory, techniques, and applications of the differential and integral calculus of functions with problems related to business, life, and the social sciences.

MCCCD Official Course Competencies
1. Find derivatives of functions using both the definition and theorems. (I)
2. Use the derivative to solve and analyze application problems related to business, life, and the social sciences. (II)
3. Use technology to model, solve, and analyze problems related to real-world applications. (II, IV)
4. Find the integral of functions using theorems. (III)
5. Use the integral to solve and analyze application problems related to business, life, and the social sciences. (IV)

MCCCD Official Course Outline
I. Derivatives
A. Limits
B. Slope and rate of change
C. Definition of the derivative
D. Rules of differentiation
1. Product
2. Quotient
3. Chain rules
4. Implicit
5. Related rates
6. Higher order
II. Applications of the Derivative
A. Increasing and decreasing functions
B. Extrema and first-derivative test
C. Concavity and second-derivative test
D. Optimization problems
E. Applications to business, life, and social sciences, including velocity and marginals
III. Integration
A. Antiderivatives and indefinite integrals, including substitution and integration by parts
B. Definite integrals and the fundamental theorem of calculus
C. Improper integrals
IV. Applications of Integration
A. Area under a curve
B. Area between two curves
C. Applications to business, life, and the social sciences

MCCCD Governing Board Approval Date: 11/24/2009

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.