MATH180

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Calculus I

MathematicsScience, Tech, Engr & Math

Overview Goals, Topics, and Objectives Assessment, Requirements, and Outcomes Register for this Course

Course Goals

To study the nature and significance of calculus for students of science, technology, engineering, and mathematics disciplines.
To demonstrate various applications of calculus to problems from the social sciences, physical sciences, and engineering.
To present an exposition of calculus that incorporates graphical, numerical, and algebraic analysis, without undue emphasis on theoretical abstraction or routine mechanical manipulation.
To use technology to illustrate calculus concepts and verify calculus solutions to application problems.
To provide students with an exposure to the logical reasoning of mathematics.

Core Course Topics

Introduction to Limits
1. Determine limits of functions using numerical, algebraic and graphical methods.
2. Determine infinite limits and limits at infinity.
3. Determine continuity or discontinuity using the limit.
Derivatives of Functions
1. Find the derivative of functions using the limit definition of the derivative.
2. Differentiate algebraic, logarithmic, exponential, trigonometric and inverse trigonometric functions using derivative rules.
3. Differentiate composite functions using the chain rule.
4. Find the derivative of a function defined implicitly.
Applications of the Derivative
1. Use the derivative to find instantaneous rates of change and related rates of change in application problems.
2. Use the derivative to find properties of functions: maxima and minima, increasing, decreasing, concavity, points of inflection and use this information to sketch the graph of functions.
3. Solve optimization problems using the derivative.
4. Determine the linear approximation of functions using the derivative.
5. Apply the Mean Value Theorem.
6. Use the derivative to define and check the antiderivative function.
Integration of Functions
1. Approximate the area under a curve using the Riemann Sum with left endpoint, right endpoint, and midpoint.
2. Find the antiderivatives (indefinite integrals) of algebraic, logarithmic, exponential, trigonometric and inverse trigonometric functions using integration rules.
3. Approximate the definite integral using the Riemann Sum with left endpoint, right endpoint, and midpoint.
4. Find the definite integral using the Fundamental Theorem of Calculus.
5. Use the integral to find the average value of a function.
6. Determine the integral of composite functions using the substitution rule.
Applications of Integration
1. Find the position and velocity functions from the acceleration function using integration.
2. Find the net rate of change of a function using integration.
3. Determine the area between two curves by integration with respect to x or y.

Learning Objectives

Upon successful completion of this course, students will be able to:

Introduction to Limits: Determine limits of functions using numerical, algebraic and graphical methods.

Introduction to Limits: Determine infinite limits and limits at infinity.

Introduction to Limits: Determine continuity or discontinuity using the limit.

Derivatives of Functions: Find the derivative of functions using the limit definition of the derivative.

Derivatives of Functions: Differentiate algebraic, logarithmic, exponential, trigonometric and inverse trigonometric functions using derivative rules.

Derivatives of Functions: Differentiate composite functions using the chain rule.

Derivatives of Functions: Find the derivative of a function defined implicitly.

Applications of the Derivative: Use the derivative to find instantaneous rates of change and related rates of change in application problems.

Applications of the Derivative: Use the derivative to find properties of functions: maxima and minima, increasing, decreasing, concavity, points of inflection and use this information to sketch the graph of functions.

Applications of the Derivative: Solve optimization problems using the derivative.

Applications of the Derivative: Determine the linear approximation of functions using the derivative.

Applications of the Derivative: Apply the Mean Value Theorem.

Applications of the Derivative: Use the derivative to define and check the antiderivative function.

Integration of Functions: Approximate the area under a curve using the Riemann Sum with left endpoint, right endpoint, and midpoint.

Integration of Functions: Find the antiderivatives (indefinite integrals) of algebraic, logarithmic, exponential, trigonometric and inverse trigonometric functions using integration rules.

Integration of Functions: Approximate the definite integral using the Riemann Sum with left endpoint, right endpoint, and midpoint.

Integration of Functions: Find the definite integral using the Fundamental Theorem of Calculus.

Integration of Functions: Use the integral to find the average value of a function.

Integration of Functions: Determine the integral of composite functions using the substitution rule.

Applications of Integration: Find the position and velocity functions from the acceleration function using integration.

Applications of Integration: Find the net rate of change of a function using integration.

Applications of Integration: Determine the area between two curves by integration with respect to x or y.