Math 5A
Broussard Fall 2008
Technical Course Information

1.        Course Number:  MATH 5A

2.        Long Course Title:  Calculus and Analytic Geometry I

3.        Short Course Title (maximum 25 characters and spaces):  Calc/Anlytc Geom I 

4.       


Units

Total Lec. Hrs.

Total Lab Hrs.

Total Other Hrs. (specify)

Total Outside of Class Hrs.

Total In & Out of Class Hrs.

Min.  5

Min.   80

Min.  0

Min. 16
Support hour

Min.  144

Min.  240

Max. 5

Max.  90

Max. 0

Max. 18
Support hour

Max.  162

Max.  270

5.        Catalog Description: 

MATH 5A
CALCULUS AND ANALYTIC GEOMETRY I
5 units
The first of a sequence of three courses in Calculus and Analytic Geometry.  Includes a review
of elementary functions, their limits, differentiation, applications of differentiation, integration,and applications of the definite integral. This course meets the CSU and UC transfer mathematics requirement and satisifies the associate degree mathematics requirement at COS. 5 hours lecture. Support hour. 
Prerequisite: MATH 4 or qualification through assessment.
Note: CAN MATH 18
Transfer Credit: CSU, UC

The first of a sequence of three courses in Calculus and Analytic Geometry.  Includes a review of elementary functions, their limits, differentiation, applications of differentiation, integration, and applications of the definite integral. Support hour.

 Math 5A is a transfer requirement for UC and CSU, required for AS degree in Mathematics at COS, foundational course for a bachelors degree in mathematics, physics, other natural sciences and business degrees, and satisfies the math general education requirement in mathematics. 

 

              
Upon entrance to this course, a student should be able to:

Student Learning Outcomes

Methods of Instruction

Methods of Evaluation/Assessment

(Must include critical thinking.
Note:  If course is being offered for COS GE credit, please include outcomes that meet all the COS GE Student Learning Outcomes.)

  • Evaluate limits by a variety of methods (COS GE Area B1).

 

  • Determine where a function is continuous methods (COS GE Area B1).
  • Compute derivatives using the limit definition and by using differentiation formulas methods (COS GE Area B1).

 

  • Find the equation of the tangent line to a function.
  • Apply derivatives to a variety of problems, including related rates and optimization problems

 

  • Use implicit differentiation
  • Compute definite integrals as a limit methods (COS GE Area B1).

 

  • Develop and solve mathematical models using the appropriate methods of calculus.
  • Appraise and justify when to apply a theorem.

 

  • Graph functions using calculus methods methods (COS GE Area B1).

 

 

The instructional methods for student learning outcomes 1 through 10 will be by instructor lecture, in-class discussions of concepts, where and when to apply the concepts, possible projects assigned for outside class, reading of the textbook out of class, and assigning homework problems.

(Must include substantial writing assignments or problem solving exercises or skill demonstrations).

Upon successful completion of the course, the student should be able to achieve the student learning outcomes and demonstrate this achievement by obtaining at least 70% accuracy on a timed test.

10.      Description of Out-of-Class Assignments.
 
Reading the textbook, homework problems assigned from the textbook or the website on a regular basis; a project, and preparation for tests and classroom presentations as required.

 

11.      Detailed Course Content (Outline Form):  If the course is repeatable, show different content for each section.

Rates of Change and Limits
Finding Limits and One-Sided Limits
Limits Involving Infinity
Continuity
Tangent Lines
Derivate as a Function
Derivate as a Rate of Change
Derivatives of Products, Quotients, and Negative Powers
Derivatives of Trigonometric Functions
The Chain Rule and Parametric Equations
Implicit Differentiation
Related rates
Extreme Values of Functions
The Mean Value Theorem and Differential Equations
The Shape of a Graph
Graphical Solutions of Autonomous Differential Equations
Modeling and Optimization
Linearization and Differentials
Newton’s Method
Indefinite Integrals, Differential Equations, and Modeling
Integral Rules; Integration by Substitution
Estimating with Finite Sums
Riemann Sums and Definite Integrals
The mean Value and Fundamental Theorems
Substitution in Definite Integrals
Numerical Integration
Volumes by Slicing and Rotation About an Axis
Modeling Volume Using Cylindrical Shells
Lengths of Plane Curves
Springs, Pumping, and Lifting
Fluid Forces
Moments and Centers of Mass

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