Syllabus Information |
Spring 2018
Apr 03, 2026 Your current Institution is CCD |
|
 |
||
 | Use this page to maintain syllabus information, learning objectives, required materials, and technical requirements for the course. |
| MAT 201 - Calculus I: MA1 |
|---|
|
Associated Term:
Spring 2018
Learning Objectives: For Required Syllabus information that is to be INCLUDED on all syllabi starting Fall 2018, 201920 please visit: https://www.cccs.edu/wp-content/uploads/documents/MAT-201-Required-Syllabi-Info-MA1.pdf REQUIRED COURSE LEARNING OUTCOMES 1. Evaluate limits using appropriate analytical, numerical or graphical techniques. 2. Analyze the continuity of functions. 3. Apply the definition and techniques of differentiation to find derivatives, including derivatives of transcendental functions. 4. Analyze functions represented by an equation or a graph using derivatives and limits. 5. Create graphs of functions using properties of derivatives and limits. 6. Apply techniques of integration to find the antiderivative of a function. 7. Evaluate definite integrals using Riemann Sums and the Fundamental Theorem of Calculus. 8. Utilize Calculus techniques to solve application problems. Required Materials: Technical Requirements: REQUIRED TOPICAL OUTLINE I. Limits using appropriate analytical, numerical or graphical techniques a. Limits computation b. Properties of limits c. Limits at infinity d. Infinite limits II. Continuity of functions a. Definition of continuity b. Discontinuities with respect to type (removable or non-removable) c. Intermediate Value Theorem III. Definition of derivative and techniques of differentiation a. The limit definition of a derivative b. Basic rules of derivatives c. Product Rule d. Quotient Rule e. Chain Rule f. Higher order derivatives g. Implicit differentiation h. Introduction of differentials i. Derivatives of trigonometric functions j. Derivatives of inverse trigonometric functions k. Derivatives of exponential and logarithmic functions IV. Functions represented by an equation or a graph using derivatives and limits a. Critical values b. Absolute extrema on an interval c. Increasing and decreasing intervals d. First and Second Derivative Tests for relative extrema e. Inflection points f. Intervals of concavity g. Graphical connection between f and f’ h. Asymptotic behavior with limits V. Graphs of functions using properties of derivatives and limits a. Graphing techniques without technology b. Graphing techniques with appropriate technology VI. Techniques of integration to find the antiderivative of a function a. Indefinite integrals b. Integration by substitution c. Integration of trigonometric functions d. Integration involving inverse trigonometric functions e. Integration involving exponential and logarithmic functions VII. Definite integrals using Riemann Sums and the Fundamental Theorem of Calculus. a. Riemann's Sums b. Definite integrals c. Fundamental Theorem of Calculus d. Integration techniques with appropriate technology VIII. Calculus techniques to solve application problems a. Mean Value Theorem b. Equations of tangent lines c. Related rates d. Rates of change e. Optimization f. Net signed area g. Area between two curves Recommended Topical Outline I. Additional limit topics a. Verify limits using the limit definition II. Integration and differentiation of additional functions. a. Hyperbolic functions III. Additional integration topics a. Numerical integration b. Mean Value Theorem for integrals c. Average Value of a function d. Techniques of integration for evaluating functions IV. Additional applications a. Volumes of revolution using disk and shell methods b. Euler's Method c. Linearization of a function d. Newton's Method e. Physics problems involving work f. Fluid: pressure and force |
| Return to Previous | New Search |
|