MATH 1081 - Single Variable Calculus I

Credits: 5
Hours/Week: Lecture None Lab None
Course Description: This is the first course in the two-semester sequence of Single Variable Calculus. Topics include functions of a single variable, limits and continuity, differentiation, antidifferentiation, and integration of algebraic and transcendental functions with associated applications in each area. A graphing calculator is required. Instruction will be provided in the use of the TI-83/TI-84 calculator. Offered F, S.
MnTC Goals
4 Mathematics/Logical Reasoning

Prerequisite(s): MATH 1062  with a grade of C or higher, or placement into MATH 1081. Restriction: Credit will not be granted for both MATH 1070  and MATH 1081.
Corequisite(s): None
Recommendation: Eligible for college-level Reading and English.

Major Content

1. Antidifferentiation, the indefinite integral
2. Application of the Definite Integral
   1. Area
3. Applications of the Derivative
   1. Elementary differential equations and their solutions
   2. Optimization
   3. Taylor polynomials
   4. Related rates
   5. Approximations
   6. Newton’s Method
4. Continuity
   1. Intuitive understanding
   2. Definition of continuity at a point
   3. Continuity on an interval and discontinuities
5. Limits
   1. Intuitive understanding
   2. Limit theorems
6. Preliminary concepts
7. The Definite Integral
   1. Intuitive understanding
   2. Approximating sums
   3. The Fundamental Theorem of calculus
8. The Derivative
   1. Intuitive or geometric interpretation
   2. Definition of the derivative
   3. Differentiation formulas
   4. Composite functions-chain rule
   5. Higher order derivatives
   6. Implicit differentiation

1. Find the area under a curve by using the Fundamental Theorem of Calculus.
2. Model and solve optimization problems by applying and analyzing the derivative.
3. Approximate the area under a curve with approximating sums by hand and with technology.
4. Analyze the geometry of a function by using differentiation.
5. Determine the derivative of a function graphically, numerically, and symbolically.
6. Demonstrate critical and logical reasoning when solving problems.
7. Find the anti-derivative of polynomials.
8. Explain the relationships between a function, its derivative, and its second derivative.
9. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.

04. 02. Clearly express mathematical/logical ideas in writing.

04. 04. Apply higher-order problem-solving and/or modeling strategies.

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