MATH 1070 - Survey of Calculus

Credits: 4
Hours/Week: Lecture None Lab None
Course Description: This course is designed for those who need only an introduction to calculus. Topics include limits and continuity, derivatives, differentials, indefinite integrals, definite integrals, exponential and logarithmic functions, techniques of integration, applications of differential and integral calculus, integral tables, functions of two variables, partial derivatives, maxima and minima, and applied problems. A graphing calculator is required. Instruction will be provided in the use of the TI-83/TI-84 calculator. Students planning to take more than one semester of calculus should begin with MATH 1081 . Offered S.
MnTC Goals
4 Mathematics/Logical Reasoning

Prerequisite(s): MATH 1061  with a grade of “C” or higher, or  placement into MATH 1070. 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. Applications of the Derivative including Maxima and Minima
2. Differentiation
   1. The derivative
   2. Derivatives of algebraic and composite functions
   3. Derivatives of higher order
3. Exponential and Logarithmic Functions
   1. Differentiation of exponential and logarithmic functions
   2. Integration of exponential and logarithmic functions
4. Functions of Two Variables
   1. Partial derivatives
   2. Relative extrema
   3. Applied problems on maxima and minima
5. Functions, Graphs and Limits
6. Integration
   1. The definite integral
   2. The fundamental theorem of integral calculus
   3. Evaluating integrals
   4. Applications
7. Techniques of Integration
   1. Substitution–change of variable
   2. Integration by parts
   3. Integration tables

1. Demonstrate critical and logical reasoning when solving problems.
2. Determine the derivative of a function graphically, numerically, and symbolically.
3. Find the derivative of algebraic and composite functions symbolically.
4. Find higher order derivatives.
5. Solve an optimization application problem by using the derivative.
6. Determine the integral of a function graphically, numerically, and symbolically.
7. Differentiate and integrate exponential and logarithmic functions
8. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
9. Determine an integral by using techniques such as substitution, integration by parts, and integration tables.
10. Find maxima and minima for functions of two variables.
11. Find partial derivative for functions of two variables.
12. Find relative extrema for functions of two variables.
13. Model and solve physics and other various application problems by applying and evaluating an integral.

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

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

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