Yuba Community College District

Yuba College Course Outline

### Course Information

Course Number: MATH 1A
Full Course Title: Single Variable Calculus I -- Early Transcendentals
Short Title: Calculus I
TOP Code: 1701.00 - Mathematics, General
Effective Term: Fall 2016

### Course Standards

Course Type: Credit - Degree Applicable
Units: 4.0
Total class hours: 216.0
Total contact hours in class: 72.0
Lecture hours: 72.0
Hours outside of class: 144.0
Repeatable: No

### Minimum Qualifications for Instructors

• Mathematics (Masters Required)

### Course Description

A first course in differential and integral calculus of a single variable: functions; limits and continuity; techniques and applications of differentiation and integration; Fundamental Theorem of Calculus. Primarily for Science, Technology, Engineering & Math Majors.

### Conditions of Enrollment

Satisfactory completion of: MATH 20; MATH 21) (Placement Exam Score)Satisfactory score on the mathematics placement test. To skip the prerequisites of Math 20 and Math 21. or

• Language - recommended eligibility for English 1A
Recommended.

### Content

Course Lecture Content
1. Definition and computation of limits using epsilon-delta, numerical, graphical, and algebraic approaches

2. Continuity and differentiability of functions
3. Derivative as a limit
4. Interpretation of the derivative as: slope of tangent line, a rate of change
5. Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule
6. Derivatives of transcendental functions such as trigonometric, exponential, logarithmic, and hyperbolic
7. Implicit differentiation with applications, and differentiation of inverse functions
8. Higher-order derivatives
9. Graphing functions using first and second derivatives, concavity and asymptotes
10. Maximum and minimum values, and optimization
11. Mean Value Theorem
12. Numerical methods to solve equations to include the Newton-Raphson method
13. Antiderivatives and indefinite integrals
14. Area under a curve
15. Definite integral; Riemann sum
16. Properties of the integral
17. Fundamental Theorem of Calculus
18. Integration by substitution
19. Indeterminate forms and L'Hopital's Rule

### Objectives

1. Compute the limit of a function at a real number.

2. Determine if a function is continuous at a real number.

3. Find the derivative of a function as a limit.

4. Find the equation of tangent line to a function.

5. Compute derivatives using differentiation formulas.

6. Use differentiation to solve applications such as related rate problems and optimization problems. **Requires Critical Thinking**

7. Solve equations numerically to include the Newton-Raphson method.

8. Use implicit differentiation.

9. Graph functions using methods of calculus. **Requires Critical Thinking**

10. Evaluate a definite integral as a limit.

11. Evaluate integrals using the Fundamental Theorem of Calculus.

12. Apply integration to find area.

### Student Learning Outcomes

1. Evaluate limits and use them to find derivatives.
2. Evaluate derivatives and interpret derivatives as rates of change and/or slopes of tangent lines.
3. Solve applications that require differentiation such as applied optimization and related rates.
4. Determine the behavior of a function from its derivatives.
5. Evaluate integrals and interpret integrals as total changes and/or bounded areas.
6. Compose simple proofs.

### Methods of Instruction

• Lecture/Discussion

### Assignments

Writing Assignments

### Methods of Evaluation

• Exams
• Homework
• Portfolio
• Problem Solving Exercises
• Quizzes
• Other
Group or individual projects.

### Course Materials

Textbooks:
1. Jon Rogawski. Calculus: Early Transcendentals, 2nd ed. Macmillan, 2012, ISBN: 978-1-4292-0838-3
Equivalent text is acceptable