May 29, 2023
MAT 201 - Calculus 1
4 Lecture Hours
Prerequisites: MAT 142 and MAT 147
A course designed for students majoring in mathematics, science or engineering. The theory of calculus, as well as problem solving and applications, is stressed. Topics include: algebraic functions; exponential and logarithmic functions; trigonometric and inverse trigonometric functions; hyperbolic and inverse hyperbolic functions; limits and continuity, derivatives and applications; curve sketching; antiderivatives; the definite integral and the Fundamental Theorem of Calculus.
Upon successful completion of the course, the student will:
- Compute limits of elementary functions.
- Apply L’Hospital’s rule to compute limits of indeterminant forms.
- Show that a function is continuous at a point in its domain.
- Compute derivatives as the limit of a difference quotient.
- Compute derivatives of elementary functions using differentiation formulas, the chain rule and implicit differentiation.
- Apply differentiation techniques to find extreme values of functions, determine the concavity of the graph and to show that a function is monotonic.
- Apply differentiation techniques to sketch the graph of a function.
- Apply the derivative to solve related rate and optimization problems.
- Compute antiderivatives of elementary functions using the substitution rule.
- Compute definite integrals by expressing them as a limit of Riemann sums.
- Compute definite integrals using the Fundamental Theorem of Calculus.
- Apply the definite integral to compute area.
- Review of the elementary functions
- Definition and computation of both finite and infinite limits, including the use of L’Hospital’s Rule
- Definition and properties of the derivative
- Differentiation rules, including the product rule, quotient rule, chain rule and implicit differentiation
- Computing derivatives of elementary functions including inverse trigonometric and hyperbolic functions
- Applying the derivative to find relative extreme values of functions, determine the concavity of the graph, find intervals of increase and decrease and to sketch the graph of a function
- Rolle’s Theorem and the Mean Value Theorem
- Application of the derivative to related rate and optimization problems
- Properties and computation of antiderivatives of elementary functions including the substitution rule
- Definition and properties of the definite integral
- Computing a definite integral as the limit of a Riemann sum
- Computing definite integrals using the Fundamental Theorem of Calculus
Each student is required to have a textbook adopted by the Mathematics Department. Students may also purchase a calculator and/or solutions manual or make use of videos and interactive software.
Approved By: Johnson, Alex Date Approved: 07/18/2013
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