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 business and 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. find coterminal angles;
2. convert from degree to radian measure and from radian to degree
measure;
3. use formulas from geometry relating to triangles to solve
real-life problems;
4. find the reference angles for given angles;
5. evaluate trigonometric functions exactly;
6. use a calculator to approximate values of trigonometric
functions;
7. use trigonometric identities to simplify and solve problems;
8. solve trigonometric equations;
9. use trigonometric functions to solve real-life problems;
10. sketch the graphs of trigonometric functions;
11. use trigonometric functions to model real-life problems;
12. evaluate limits involving trigonometric functions;
13. use the rules for differentiation to find the derivatives of
functions involving trigonometric functions;
14. use calculus to analyze the graphs of functions that involve
trigonometric functions;
15. use techniques of integration to find antiderivatives of
functions that involve trigonometric functions;
16. evaluate definite integrals involving trigonometric functions;
17. use calculus to solve application problems involving
trignonometric functions;
18. plot points in space;
19. find the distance between two points in space;
20. write the general form of the equation of a plane;
21. write the standard form of the equation of a sphere;
22. sketch planes in space;
23. sketch the coordinate plane traces of quadric surfaces;
24. classify quadric surfaces in space;
25. evaluate functions of several variables;
26. find the domains and ranges of functons of two variables;
27. sketch the level curves of functions of two variables;
28. use functions of several variables to answer questions about
real-life situations;
29. find the first partial derivatives of functions of several
variables;
30. find the slopes of surfaces in particular directions;
31. find the second partial derivatives of functions of several
variables;
32. use partial derivatives to answer questions about real-life
situations;
33. find the relative extrema of functions of two variables;
34. use relative extrema to answer questions about real-life
situations;
35. use Lagrange multipliers to find extrema of functions of several
variables;
36. use Lagrange multipliers to answer questions about real-life
situations;
37. evaluate double integrals;
38. use double integrals to find the area of regions in the plane;
39. use double integrals to find the volume of solid regions;
40. verify that an equation is a solution of a differential
equation;
41. find general solutions of differential equations;
42. use initial conditions to find particular solutions of
differential equations;
43. use particular solutions to answer questions about real-life
situations;
44. solve differential equations whose variables are separable;
45. use separable variable differential equations to answer
questions about real-life situations;
46. solve first-order linear differential equations;
47. solve differential equations using integrating factors;
48. use differential equations to model real-life situations;
49. find the terms of sequences;
50. determine the convergence or divergence of sequences;
51. find the limits of convergent sequences;
52. find patterns for sequences;
53. use sequences to answer questions about real-life situations;
54. find the partial sums of sequences;
55. determine the convergence or divergence of infinite series;
56. use the nth-term test to show that series diverge;
57. find the nth partial sums of geometric series;
58. determine the convergence or divergence of geometric series;
59. use geometric series to model real-life situations;
60. determine the convergence or divergence of p-series;
61. use the ratio test to determine the convergence or divergence of
series;
62. find the radii of convergence of power series;
63. use Taylor''s theorem to find power series for functions;
64. use a basic list of power series to find power series for
functions;
65. find Taylor polynomials for functions;
66. use Taylor polynomials to approximate functions; and
67. approximate definite integrals using Taylor polynomials.

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. 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
II. 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
III. 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
IV. 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: (Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour. List types of assignments, including library assignments.)

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

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

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

SECTION D

SECTION E

SECTION F

SECTION G