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1. Division:

  Sciences & Mathematics

2. Course Discipline:


3. Course Number:


4. Course Title:


5. First semester this new version/new course will be offered: Fall 2018




General Course Information


1. Units: 4.0                 Variable units N/A

2. This Course is:

Degree-Applicable Credit - Transferable


3A.  Cross-List: 


3B.  Formerly:




Course Format and Duration


4. Standard Term Hrs per Wk


5. Standard Term Total Semester Hrs
















By Arrangement:



By Arrangement:


Total Hrs per Wk



Total Hrs



6. Minimum hours per week of independent work done outside of class:    8


Course Preparation – (Supplemental form B required)


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 30 with 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”.)

Completion of MATH 27 with grade of "C" or better




Catalog Description And Other Catalog Information


8. Repeatability:

Not Repeatable

Please Note: 8. (Repeatability) does not refer to repeating courses because of substandard grades or a lapse of time since the student took the course. A course may be repeated only if the course content differs each time it is offered and the student who repeats it is gaining an expanded educational experience as stipulated in Title 5.


Skills or proficiencies are enhanced by supervised repetition and practice within class periods.

Active participatory experience in individual study or group assignments is the basic means by which course objectives are attained.

Course content differs each time it is offered.


Explanation for above repeatability selection:


9a. Grading Option:

Standard Grade

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.




Course Outline Information


10. Course Objectives: (Course objectives for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Course objectives 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 trigonometric 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 Out-of-Class Assignments: Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour, less for lab/activity classes.  List types of assignments, including library assignments.)


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

1. Read in your textbook about 2 methods for calculating the volume of a solid of revolution and be prepared for a class discussion.
2. Research online the history of Newton's discovery of the Binomial Series and be prepared to discuss in class.


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

1. Write a 3 - 5 page report on Newton's discovery of the Binomial Series.
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 extrema of the function y = x - sinx over the interval (0, 2pi).


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


13. Required Materials:

a. All Textbooks, resources and other materials used in this course are College Level?




b. Representative college-level textbooks (for degree-applicable courses) or other print materials.

Book 1:


  Larson, Edwards


  Calculus, An Applied Approach


  Brooks Cole Cengage Learning

Date of Publication:




Book 2:







Date of Publication:




Book 3:







Date of Publication:




Book 4:







Date of Publication:




Book 5:







Date of Publication:




c. Other materials and/or supplies required of students:


Methods of Instruction


14a. Check all instructional methods used to present course content.


Laboratory and/or Activity

Distance Learning (requires supplemental form)




14b. Provide specific examples for each method of instruction checked above; include a minimum of two examples total. Reference the course objective(s) addressed by instructional method(s). Explain both what the instructor and students are expected to be doing and experiencing.

Example 1: Interactive lecture format to develop the concept of finding a power series representation of a variety of functions. For each type of function, the instructor will incorporate algebraic derivation and visual analysis though graphing. Students will participate verbally and will work several examples on their own.

Example 2: In class, small group collaborative learning activities will focus on determining which methods of integration to use for a variety of problems, for example Use solids of revolution to solve real-life problems. Students will practice recognizing which method to try, testing their conjectures, and developing solutions with peers.




15. Methods of Assessing Student Learning  


15a.  Methods of Evaluation:


Essay Examinations

Objective Examinations

Problem Solving Examinations

Skill Demonstrations



Classroom Discussions




Other (explain below)







15b. Based upon course objectives, give examples of how student performance will be evaluated. Provide examples for each method checked above; include a minimum of two examples total.




Example 1: The line segment from (0, 0) to ( 4, 2) is revolved about the y axis to form a cone. Find the volume of the cone. This question is graded based on the clarity, completeness, and correctness of the method used and of the solutions found.

Example 2: Find the area of the region bounded by the graphs of the equations y = xlnx, x = 3, x = 5 using integration by parts. This question is graded based on the clarity, completeness, and correctness of the method used and of the solutions found.

Example 3: Classify the surface given by x^2 + y^2 – z^2 = 1. Describe the traces of the surface in the xy-plane, the yz-plane and the xz-plane. (from outcome 8). This question is graded based on the clarity, completeness, and correctness of the method used and of the solutions found.

Example 4: Have the students construct a model of a saddle point using the media of their choice.

Example 5: Have the students find an application of a topic in their field and make a poster presenting their information.












1. Program Information:  

In an approved program.  

Part of a new program.

Not part of an approved program.  

2. Course TOP Code:

   Program title - TOP Code:  

Mathematics, General- 170100


3. Course SAM Code:

 A  Apprenticeship

 B  Advanced Occupational

 C  Clearly Occupational

 D  Possibly Occupational

 E  Non-Occupational


4. Faculty Discipline Assignment(s):










General Education Information:  

1.  College Associate Degree GE Applicability:    

Communication & Analytic Thinking
Math Competency

2.  CSU GE Applicability (Recommended-requires CSU approval):

B-4 Mathematics/Quantitative Reasoning

3.  IGETC Applicability (Recommended-requires CSU/UC approval):  

2: Mathematical Concepts & Quantitative Reasoning

4. C-ID:  






Articulation Information:  (Required for Transferable courses only)



CSU Transferable.  

UC Transferable.

CSU/UC major requirement.  


If CSU/UC major requirement, list campus and major. (Note: Must be lower division)




List at least one community college and its comparable course.  If requesting CSU and/or UC transferability also list a CSU/UC campus and comparable lower division course.


American River College: Math 351 Calculus for Life and Social Sciences II
Cal Poly SLO: MATH 162 Calculus for the Life Sciences II
UC Berkeley: MATH 16B Analytic Geometry and Calculus
UC Davis: MATH 16C Short Calculus





Planning and Resources - Please address the areas below:  

1. Evidence of Planning: connection to existing or planned degrees/certificates, place in general education; relationship to mission (basic skills, transfer, career technical education, lifelong learning); transfer university requirements; advisory/regional/national needs; or other planning considerations.

Satisfies short calculus requirement for a variety of majors.
Transfer level math class.
Meets GE applicability for Math Competency and Communication and Analytical Thinking. Course includes all four math program's SLO's. (Equations and Expressions, Visual Models, Applied Problems, Communication.)

2. Potential Impact on Resources: faculty, facilities, computer support/lab, library, transportation, equipment, or other needs.
All math faculty members meet the minimum qualifications to teach this course. No special training is required.
No additional resources are needed since we have the classroom space and technology already available.





1.  Maximum Class Size (recommended):              35

2.  If recommended class size is not standard, then provide rationale: