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Nov 21, 2024
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MAT 201 - Calculus 1
Credits: 4
4 Lecture Hours
Prerequisites: MAT 142 and MAT 147
Description
This course is for students majoring in mathematics, science or engineering. The theory of calculus, as well as problem solving and applications, is stressed. Students explore topics including algebraic, exponential and logarithmic functions. Additionally, students learn to solve trigonometric and inverse trigonometric functions, hyperbolic and inverse hyperbolic functions and curve sketching. Students learn to apply limits and continuity, applications of derivatives and antiderivatives. The definite integral and the Fundamental Theorem of Calculus are also discussed.
Learning Outcomes
Upon successful completion of the course, the student will:
- Compute limits of algebraic and transcendental functions, including indeterminate forms.
- Verify whether a function is continuous at a point.
- Compute derivatives using the definition, the differentiation formulas and implicit differentiation.
- Analyze derivatives to sketch a function’s graph.
- Solve related rate and optimization problems.
- Implement Riemann Sums and the Fundamental Theorem of Calculus to solve definite integrals.
Listed Topics
- Finite and infinite limits, including L’Hospital’s Rule
- Continuity
- Definition and properties of the derivative
- Differentiation rules applied to algebraic and transcendental functions, including the product rule, quotient rule, chain rule and implicit differentiation
- Relative and extreme values, concavity and intervals of increase and decrease of a function
- Sketching a function’s detailed graph using calculus
- Rolle’s Theorem and the Mean Value Theorem
- Related rates and optimization problems
- Computation of antiderivatives of algebraic and transcendental functions
- The definite integral defined as the limit of a Riemann Sum
- The Fundamental Theorem of Calculus
Reference Materials
Each student is required to have a textbook/e-book/online homework system adopted by the Mathematics Department.
Students who successfully complete this course acquire general knowledge, skills and abilities that align with CCAC’s definition of an educated person. Specifically, this course fulfills these General Education Goals: - Critical Thinking & Problem Solving
- Quantitative & Scientific Reasoning
Approved By: Dr. Quintin B. Bullock Date Approved: 5/8/2023
Last Reviewed: 5/8/2023
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