MATH 1133 - Calculus I
5 Credits
Provides an introduction to single variable calculus and prepares students for Calculus II (MATH 1134 ). The topics include limits, derivatives (including trigonometric, logarithmic and exponential functions), continuity, applications of derivatives to related rates and optimization, graphing using information from the first and second derivatives, separable differential equations, Riemann Sums, basic integration techniques (including substitution), definite integrals, the Fundamental Theorem of Calculus, Trapezoidal and Simpson’s Rule. Students will become proficient with a computer algebra system. Use of technology will be embedded throughout the course.
Pre-Requisites MATH 1127 , MATH 1119
Major Content Areas
Limits.Derivatives. Application of Differentiation .Basic integration techniques, including substitution. Approximation techniques. Differential Equations.
Learning Outcomes
Use the first and/or second derivative tests and limits to analyze important features of the graph of a function. Recognize limits in indeterminate forms (quotient, product, difference, power) and apply L’Hospital’s Rule appropriately to evaluate them. Define the definite integral as a limit of Riemann sums. Describe the relationship between derivative and definite integral as expressed in both parts of the Fundamental Theorem of Calculus, and apply it to evaluate definite integrals using antiderivatives. Evaluate indefinite integrals, including u-substitution technique. Explain the concept of limit from a graphical, numerical, and algebraic point of view. Be able to illustrate and calculate limits of a variety of algebraic and transcendental functions, and limits involving infinity. Describe what it means for a function to be continuous. Identify various types of discontinuities. Compute a derivative using the definition. Find derivatives using differentiation rules and implicit differentiation. Recognize the derivative as a rate of change and a slope. Use derivatives to solve application problems such as optimization and related rates.
Minnesota Transfer Curriculum (MNTC) Goals
04 - Mathematical/Logical Reasoning 02 - Critical Thinking
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