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
Effective Term:
Fall 2016
Course Standards
Lecture Hours:
72.000
Total Units:
4.000
Total Hours:
72.00
Repeatable:
No
Grading Method:
Letter Grade or Pass/No Pass
Minimum Qualifications
 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
Completion with a C or better in: MATH 20; MATH 21). Other: (Placement Exam Score)Satisfactory score on the mathematics placement test.
To skip the prerequisites of Math 20 and Math 21. or
Advisories

Language  recommended eligibility for English 1ARecommended.
Content
Course Lecture Content

Definition and computation of limits using epsilondelta, numerical, graphical, and algebraic approaches
 Continuity and differentiability of functions
 Derivative as a limit
 Interpretation of the derivative as: slope of tangent line, a rate of change
 Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule
 Derivatives of transcendental functions such as trigonometric, exponential, logarithmic, and hyperbolic
 Implicit differentiation with applications, and differentiation of inverse functions
 Higherorder derivatives
 Graphing functions using first and second derivatives, concavity and asymptotes
 Maximum and minimum values, and optimization
 Mean Value Theorem
 Numerical methods to solve equations to include the NewtonRaphson method
 Antiderivatives and indefinite integrals
 Area under a curve
 Definite integral; Riemann sum
 Properties of the integral
 Fundamental Theorem of Calculus
 Integration by substitution
 Indeterminate forms and L'Hopital's Rule
Objectives

Compute the limit of a function at a real number.

Determine if a function is continuous at a real number.

Find the derivative of a function as a limit.

Find the equation of tangent line to a function.

Compute derivatives using differentiation formulas.

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

Solve equations numerically to include the NewtonRaphson method.

Use implicit differentiation.

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

Evaluate a definite integral as a limit.

Evaluate integrals using the Fundamental Theorem of Calculus.

Apply integration to find area.
Student Learning Outcomes
 Evaluate limits and use them to find derivatives.
 Evaluate derivatives and interpret derivatives as rates of change and/or slopes of tangent lines.
 Solve applications that require differentiation such as applied optimization and related rates.
 Determine the behavior of a function from its derivatives.
 Evaluate integrals and interpret integrals as total changes and/or bounded areas.
 Compose simple proofs.
Methods of Instruction

Lecture/Discussion
Assignments
Hours per week on assignments outside of the class:
Reading Assignments
Writing Assignments
Methods of Evaluation
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes

OtherGroup or individual projects.
Course Materials
Textbooks:

Jon Rogawski. Calculus: Early Transcendentals, 2nd ed. Macmillan, 2012, ISBN: 9781429208383Equivalent text is acceptable