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

Three years of high school mathematics which includes two years of algebra & placement by the matriculation assessment process, or Math. 12, 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”.)

Not open to students with a grade of "C" or better in Math. 30 or equivalent

9b. Catalog Description:

Review of functions, limits, differentiation of algebraic functions, analytic geometry, integration of algebraic functions, calculus for exponential and logarithmic functions, applications of calculus in business and the social and life sciences. This course is not intended for students majoring in mathematics, engineering, physics, or chemistry. (CAN MATH 30) (With Math 16B, 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. sketch the graph of a function by hand or using a graphing
utility;
2. interpret functions and real-life data that are presented
graphicaly;
3. find the points of intersection of two functions algebraically
and graphically;
4. use linear and quadratic functions to solve application
problems;
5. combine functions to form other functions;
6. find the inverse of a function when it exists;
7. determine whether a limit exists;
8. evaluate the limit of a function;
9. determine whether a function is continuous at a point, in an
open interval, and in a closed interval;
10. find the intervals on which a function is continuous;
11. interpret the slope of a graph in a real-life setting;
12. use the limit definition to find the derivative of a function;
13. use the derivative to find the slope of a graph at a point;
14. use the derivative to find an equation of a tangent line to a
graph at a point;
15. use the graph of a function to recognize points at which the
function is not differentiable;
16. use the rules for differentiation to find the derivative of
a function;
17. find the average and instantaeous rates of change of a quantity
in an application problem;
18. find higher-order derivatives;
19. find and use the position function to determine the velocity and
acceleration of a moving object;
20. find derivatives implicitly;
21. solve related rate problems;
22. find the critical numbers of a function;
23. find the open intervals on which a function is increasing or
decreasing;
24. find intervals on which a real-life model is increasing or
decreasing;
25. use the first-derivative test to find the relative extrema of a
function;
26. find the absolute extrema of a continuous function on a closed
interval;
27. find minimum and maximum values of a real-life model and
interpret the results in context;
28. find the open intervals on which the graph of a function is
concave upward or concave downward;
29. find the points of inflection of the graph of a function;
30. use the second-derivative test to find the relative extrema of a
function;
31. solve real-life optimization problems;
32. use derivatives to sketch the graph of a function;
33. find infinite limits and limits at infinity;
34. find the vertical and horizontal asymptotes of a rational
function and sketch its graph;
35. use asymptotes to answer questions about real-life situations;
36. analyze the graph of a function;
37. find the differential of a function;
38. use differentials to approximate changes in a function;
39. use basic integration formulas to find antiderivatives;
40. use initial conditions to find particular solutions of indefinte
integrals;
41. use antiderivatives to solve real-life problems;
42. use the general power rule to find antiderivatives;
43. use the fundamental theorem of calculus to evaluate a definite
integral;
44. find the area of a region bounded by the graph of a function and
the x-axis;
45. find the area of a region bounded by two graphs;
46. use the area of a region to solve real-life problems;
47. use the disc method to find the volume of a solid of revolution;
48. use the washer method to find the volume of a solid of revolution;
49. use solids of revolution to solve real-life problems;
50. use substitution to find antiderivatives;
51. use substitution to evaluate definite integrals;
52. use integration by parts to find antiderivatives;
53. use partial fractions to find antiderivatives;
54. use integration tables to find antiderivatives;
55. use integration to solve real-life problems;
56. evaluate improper integrals with infinite limits of integration;
57. evaluate improper integrals with infinite integrands;
58. use improper integrals to solve real-life problems;
59. use properties of exponents to answer questions about real-life
situations;
60. sketch the graphs of exponential functions;
61. evaluate limits of exponential functions;
62. sketch the graphs of logistics growth functions;
63. use logistics growth functions to model real-life situations;
64. answer questions involving the natural exponential function as a
real-life model;
65. find the derivatives of natural exponential functions;
66. use calculus to analyze the graphs of functions that involve the
natural exponential funciton;
67. sketch the graphs of natural logarithmic functions;
68. use properties of natural logarithms to answer questions about
real-life situations;
69. find the derivatives of natural logarithmic functions;
70. use calculus to analyze the graphs of functions that involve the
natural logarithmic function;
71. find the derivatives of exponential and logarithmic functions
involving other bases;
72. use exponential growth and decay to model real-life situations;
73. use the exponential and logarithmic rules to find antiderivatives;
74. evaluate definite integrals involving exponential and
logarithmic functions; and
75. use calculus to solve application problems involving exponential
and logarithmic functions.

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. Review of Functions and Graphs
A) Rectangular Coordinate System
B) Graphs of Equations
C) Linear Functions
D) Quadratic Functions
E) Composite Functions
F) Inverse Functions
II. Limits
A) Limit of a Function
B) Propeties of Limits
C) Evaluating Limits
D) One-sided Limits
E) Existence of a Limit
III. Continuity
A) Definition of Continuity
B) Determining Continuity of a Function
C) Continuity on a Closed Interval
D) Discontinuity
IV. Differentiation
A) Tangent Line to a Graph
B) Definition of the Derivative
C) Differentiability and Continuity
D) Rules for Differentiation
1. The constant rule
2. The constant multiple rule
3. The sum and difference rules
4. The power rule
5. The product and quotient rules
6. The chain rule
E) Rates of Change
F) Higher-Order Derivatives
G) Implicit Differentiation
H) Related Rates
V. Applications of the Derivative
A) Increasing and Decreasing Functions and Intervals
B) Relative and Absolute Extrema
C) Concavity and Points of Inflection
D) Curve Sketching
E) Optimization Problems
F) Differentials
VI. Integration
A) Antiderivatives
B) Indefinte 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
VII. 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
VIII. Calculus of Exponential and Logarithmic Functions
A) Review of Exponential and Logarithmic Functions
B) Derivatives of Exponential and Logarithmic Functions
C) Exponential Growth and Decay
D) Integrals of Exponential and Logarithmic Functions
E) Applications involving Exponential and Logarithmic
Functions

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