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Math 125 syllabus
Calculus I
Course Description: The course provides an introduction to calculus with emphasis on differential calculus. Topics include limits of functions, derivatives of algebraic and transcendental functions, application of the derivative to curve sketching, optimization problems, and examples in the natural sciences, engineering, and economics. The course concludes with an introduction to anti-derivatives, definite integrals, and the fundamental theorem of calculus. Credit for both MA 120 and MA 125 is not allowed. Core Course.
Prerequisites: ACT Math 27 or MyMathTest 090 or MA 113 Minimum Grade of C or MA 115 Minimum Grade of C or SAT Mathematics 665 or MATH SECTION SCORE 695.
Textbook: Joel Hass and Maurice D. Weir: University Calculus – Early Transcendentals, Pearson, 4th edition, 2020
Coverage: Chapter 1 (1.3, 1.5, 1.6), Chapter 2 (2.2, 2.4-2.6), Chapter 3 (3.1-3.3, 3.5-3.11), Chapter 4 (4.1-4.8), Chapter 5 (5.1-5.5)
Calculator: A TI-30XIIS calculator is permitted to be used in this course.
Homework: Common homework is available through MyLabsPlus.
Learning outcomes: Upon the successful completion of the course a student will:
- Evaluate Limits Using Graphs
- Evaluate Limits of Rational Functions Using Algebraic Cancellation
- Evaluate Limits of Trigonometric Functions
- Determine Where a Function is Continuous
- Find Continuous Extensions of Functions
- Evaluate Limits Involving Infinity and Identify Asymptotes
- Compute the Derivative of a Function at a Point Using the Limit Definition
- Graphically Determine Where a Function is Differentiable
- Graphically Interpret the Derivative of a Function
- Compute the Derivative of Polynomial, Trigonometric, Exponential, and Logarithmic Functions
- Compute the Derivative of Algebraic Combinations of Functions
- Compute the Derivative of the Composition of Functions
- Compute the Derivative of Function Implicitly Defined by Curves
- Apply the Derivative to Find the Rate of Change of Real World Situations with Interconnected Parts
- Determine the Intervals on Which a Function is Increasing and Decreasing and Use the First Derivative to Identify
- Minimums and Maximums
- Determine the Intervals on Which a Function is Concave Up and Concave Down and Use the Second Derivative to
- Identify Minimums and Maximums
- Apply the Derivative to Sketch the Graph of a Function
- Apply the Derivative to Optimize Real World Situations
- Approximate the Area Under a Curve
- Compute the Antiderivative of Polynomial, Trigonometric, and Exponential Functions
- Apply the Fundamental Theorem of Calculus to Evaluate Definite Integrals
- Solve Initial Value Problems
Secondary Learning Outcomes:
- Apply the Intermediate Value Theorem to Approximate the Solutions to Equations Involving Continuous Functions
- Compute the Derivative of Inverse Functions
- Generate a Linear Approximation to a Differentiable Function
- Apply Newton’s Method to Approximate the Zeros of a Differentiable Function
- Apply the Mean Value Theorem to Infer the Rate of Change
- Apply the Extreme Value Theorem to Argue for the Existence of Maximums and Minimums
- Apply L’Hopital’s Rule to Evaluate Limits of Indeterminate Form
Learning Outcomes for Quantitative Reasoning:
- Convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, tables, words).
- Solve mathematical problems.