7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math. 16A or Math. 30 or equivalent with a grade of "C" or better

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

Trigonometry (Math. 8) is recommended. Not open to students with a grade of "C" or better in Math. 31 or equivalent

9b. Catalog Description:

Differentiation and integration of trigonometric functions, functions of several variables, partial derivatives, double integrals, introduction to differential equations, sequences and series, applications of calculus in the social and life sciences. (CAN MATH 32) (With Math 16A, CAN MATH SEQ D)

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

1. Apply the Fundamental Theorem of Calculus.
2. Use the disc method and washer method to find the volume of a solid of revolution. Use solids of revolution to solve real-life problems.
3. Use integration by substitution, integration by parts, partial fractions, and integration tables to find antiderivatives. Use techniques to solve real–life problems.
4. Evaluate improper integrals with infinite limits of integration and infinite integrands. Solve real-life problems.
5. Evaluate trigonometric functions (exactly and approximately), their limits and their derivatives. Calculate using degrees and radians.
6. Solve trigonometric equations (including real life applications) using identities and special angles.
7. Sketch the graphs of trigometric functions using calculus when necessary.
8. Analyze points (distance between and midpoint) and surfaces (spheres, planes, traces, level curves) and graphs (quadric surfaces) in the three dimensional coordinate system.
9. Calculate partial derivatives and find extrema of functions of several variables including real life examples.
10. Use Lagrange multipliers to solve constrained optimization problems.
11. Evaluate double integrals and use them to find area and volume.
12. Find general solutions and particular solutions of differential equations. Solve differential equations using separation of variables and integrating factors. Use differential equations to model and solve real-life problems.
13. Find the limit of a sequence of numbers and use techniques to solve business and economic applications involving sequences.
14. Determine the convergence or divergence of an infinite series. Use the Ratio Test and Convergence Test to determine convergence or divergence for p-series.
15. Use Taylor's Theorem to determine the Taylor and Maclaurin series of simple functions.
16. Use Taylor polynomials for approximation.
17. Use the Power Rule, Exponential Rule and Log Rule to calculate antiderivatives.
18. Evaluate definite integrals to find the area bounded by two graphs.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Integration
A) Antiderivatives
B) Indefinite Integrals
C) Integration Rules
1. The constant rule
2. The constant multiple rule
3. The sum and difference rules
4. The power rule
D) Integrating by Substitution
E) Area and Definite Integrals
F) The Fundamental Theorem of Calculus
II. Applications and Techniques of Integration
A) The Area of a Region
B) The Volume of a Solid of Revolution
C) Integration by Substitution
D) Integration by Parts
E) Partial Fractions
F) Integration Tables
G) Improper Integrals
III. Calculus of Trigonometric Functions
A) Introduction to Trigonometric Functions
B) Trigonometric Identities
C) Evaluating Trigonometric Functions
D) Solving Trigonometric Equations
E) Graphs of Trigonometric Functions
F) Limits of Trigonometric Functions
G) Derivatives of Trigonometric Functions
H) Integrals of Trigonometric Functions
I) Applications Involving Trigonometric Functions
IV. Calculus of Functions of Several Variables
A) The Three-Dimensional Coordinate System
B) Surfaces in Space
C) Equations of Planes in Space
D) Equations of Quadric Surfaces
E) The graph of a Function of Two Variables
F) Partial Derivatives
G) Extrema of Functions of Two Variables
H) Optimization Problems
I) Constrained Optimization Problems
J) Lagrange Multipliers
K) Double Integrals
L) Area in the Plane
M) Volume of a Solid Region
V. Introduction to Differential Equations
A) General Solution of a Differential Equation
B) Particular Solutions of a Differential Equation
C) Solving Differential Equations using Separation of Variables
D) First-Order Linear Differential Equations
E) Solving Differential Equations using Integrating Factors
F) Applications of Differential Equations
VI. Sequences and Series
A) Definition of a Sequence
B) Limit of a Sequence
C) Infinite Series
D) Properties of Infinite Series
E) Geometric Series
F) p-Series
G) Convergence and Divergence of an Infinite Series
H) The Ratio Test
I) Power Series
J) Radius of Convergence of a Power Series
K) Taylor and Maclaurin Series
L) Taylor Polynomials

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

1. Students will read the text book and solve problems based on reading.
2. Read supplementary handouts on topics such as volumes of solids of revolution and be able to solve problems using both washer and disk method.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Find the standard form of the equation of a sphere whose center is at the point ( 1, -3, 4) and whose radius is 3.
2. A 20-foot ladder leaning against the side of a house makes a 75 degree angle with the ground. How far up the side of the house does the ladder reach?
3.Find the relative extrama of the function y = x - sinx over the interval (0, 2pi).

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G