MATH A180: Calculus 1
| Item | Value |
|---|---|
| Curriculum Committee Approval Date | 02/23/2022 |
| Top Code | 170100 - Mathematics, General |
| Units | 5 Total Units |
| Hours | 90 Total Hours (Lecture Hours 90) |
| Total Outside of Class Hours | 0 |
| Course Credit Status | Credit: Degree Applicable (D) |
| Material Fee | No |
| Basic Skills | Not Basic Skills (N) |
| Repeatable | No |
| Grading Policy | Standard Letter (S),
|
| Associate Arts Local General Education (GE) |
|
| Associate Science Local General Education (GE) |
|
| California General Education Transfer Curriculum (Cal-GETC) |
|
| Intersegmental General Education Transfer Curriculum (IGETC) |
|
| California State University General Education Breadth (CSU GE-Breadth) |
|
Course Description
This is the first course in the calculus sequence. It satisfies the sequence for majors in mathematics, science, or engineering. Topics include limits, derivatives of algebraic and transcendental functions, applications of derivatives, indefinite integrals, definite integrals, the Fundamental Theorem of Calculus, and applications of integration. Enrollment Limitation: MATH A180H; students who complete MATH A180 may not enroll in or receive credit for MATH A180H. PREREQUISITE: MATH A170 or appropriate placement. Transfer Credit: CSU; UC: Credit Limitation: MATH A140, MATH A180, MATH A180H and MATH A182H combined: maximum credit, 1 course; MATH A180/H, MATH A185/H combined are equivalent to MATH A182H. C-ID: MATH 210.C-ID: MATH 210.
Course Level Student Learning Outcome(s)
- Calculate limits when they exist, and explain why when they do not.
- Determine where a function is continuous and/or differentiable, and explain why.
- Compute derivatives of polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions.
- Use techniques of differentiation, including the product, quotient, and chain rules, and implicit differentiation.
Course Objectives
- 1. State and apply the definitions of limits, derivatives, definite integrals and indefinite integrals.
- 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 a tangent line to a function.
- 5. Compute the limit of a function with and without using LHospitals Rule.
- 6. Calculate derivatives of algebraic and transcendental functions using the definition, the sum rule, the product rule, the quotient rule and the chain rule.
- 7. Use implicit differentiation.
- 8. Solve certain types of derivative applications such as related rates problems, linear approximations to functions and optimization problems.
- 9. Graph functions by applying information obtained from the first and second derivative.
- 10. Calculate definite integrals using the definition, formulas, Riemann Sums and simple substitutions.
- 11. Evaluate definite integrals using the Fundamental Theorem of Calculus and using the Substitution Method.
- 12. Calculate indefinite integrals using the definition, formulas and simple substitutions.
- 13. Use definite integrals in terms of either x or y to computer areas and volumes.
- 14. Use definite integrals to compute work and the average value of a function.
Lecture Content
Functions and Models Functions, domains and ranges Catalog of functions: polynomial, rational, algebraic and transcendental Inverse functions and their properties Review of properties of exponential and logarithmic functions Development of the inverse trigonometric functions and their properties Limits and Rates of Change Two-sided limits and one-sided limits with graphical interpretations Computing limits using sum, difference, product, quotient and other rules Computing limits indirectly using the "Squeeze" theorem and other methods Formal ., . definitions of limits Given a linear function and its limit, compute . for given values of . Given a linear function and its limit, compute . in terms of an arbitrary . Definition of continuity, a survey of continuous functions, and the Intermediate Value Theorem The definition of limits as x.± . and its graphical interpretation as horizontal asymptotes Slopes of tangent lines and velocities as applications of limits Derivatives The definition of the derivative of a function Computing derivatives using only the limit definition Derivative formulas for monomial, trigonometric, exponential, logarithmic and hyperbolic functions Discussion of the power rule, sum rule, product rule and quotient rule with examples Discussion of the chain rule with examples Computing derivatives using implicit differentiation Computing higher order derivatives explicitly and implicitly Related rates applications Differentials and their use as estimations in applications Newtons Method Applications of the Derivative Id entifying critical numbers, local extrema and absolute extrema Rolles Theorem, the Mean Value Theorem, and applications of these theorems Identifying intervals where ƒ (x) is increasing or decreasing The First Derivative Test for identifying local extrema Concavity and points of inflection The Second Derivative Test for identifying local extrema LHospitals Rule and indeterminate forms Curve sketching identifying local and absolute extrema, intervals where the graph is increasing or decreasing, concavity, inflection points and asymptotes Optimization applications from the sciences and economics Antiderivatives as an example of a basic differential equation Integrals Summation notation and properties of finite sums Areas computed as Riemann sums Definition of the definite integral as a limit of a Riemann sum Properties of definite integrals The Fundamental Theorem of Calculus Computation of definite integrals using the Fundamental Theorem of Calculus Using u-substitution in definite and indefinite integrals Applications of Integration Computing area between curves by constructing definite integrals and integrating with respect to x or y Computing volumes of solids of revolution by constructing definite integrals using the methods of cross-sections or disks and integrating with respect to x or y Computing volumes of solids of revolution by constructing definite integrals using the methods of washers or shells and integrating with respect to x or y Computing work by constructing definite integrals and integrating with respect to x or y Computing the average value of a function over a closed interval by constructing definite integrals and integrating with respect to x or y
Method(s) of Instruction
- Lecture (02)
Instructional Techniques
The primary mode of instruction is the lecture/demonstration method. Some sections may utilize graphing calculators.
Reading Assignments
From assigned text. 1 hour
Writing Assignments
Problem solving exercises commonly appear on exams or quizzes. These require written responses of the students. Critical thinking is an integral part of a calculus course. 1 hour
Out-of-class Assignments
Homework assignments as given by instructor. 6 hours
Demonstration of Critical Thinking
Grades are determined by performance on quizzes and exams. Some instructors may also include grades on homework, cooperative assignments, or participation in cooperative learning sessions. A comprehensive final exam is part of this course.
Required Writing, Problem Solving, Skills Demonstration
Problem solving exercises commonly appear on exams or quizzes. These require written responses of the students. Critical thinking is an integral part of a calculus course.
Eligible Disciplines
Mathematics: Masters degree in mathematics or applied mathematics OR bachelors degree in either of the above AND masters degree in statistics, physics, or mathematics education OR the equivalent. Masters degree required.
Textbooks Resources
1. Required Stewart, James. Calculus, Early Transcendentals , 9th ed. Cengage Publishing, 2019 Rationale: -
Other Resources
1. Other appropriate textbook as chosen by faculty.