The student will be able to:

1. Define the antiderivative and determine antiderivatives of simple functions.
2. Demonstrate an understanding of and evaluate and approximate definite integrals.
3. Find antiderivatives graphically and analytically.
4. Use the first and second fundamental theorems of calculus to evaluate definite integrals and construct antiderivatives.
5. Evaluate a definite integral as a limit.
6. Apply integration to find area.
7. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
8. Apply integration to areas and volumes, and other applications such as work or length of a curve.
9. Evaluate improper integrals.
10. Graph and differentiate functions in polar and parametric form.
11. Graph and integrate functions in polar and parametric forms.
12. Solve and interpret solutions to elementary differential equations.
13. Use technology, such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (1) through (12) above.
14. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
15. Interpret mathematical solutions.

1. Define the antiderivative and determine antiderivatives of simple functions
   1. Find general antiderivatives
   2. Antiderivatives in the context of rectilinear motion
   3. Graphing antiderivatives
   4. Families of curves
2. Demonstrate an understanding of and evaluate and approximate definite integrals
   1. Signed area under a curve and the net change of a function F from f
   2. Properties of integrals
   3. Approximating definite integrals
   4. Interpretations of the definite integral
   5. Average value of a function
   6. Numerical approximations to definite integrals using rectangular, trapezoidal and Simpson's approximation and estimation of errors
3. Find antiderivatives graphically, and analytically
   1. The graphical relationship between a function and its antiderivatives
   2. Construction of antiderivatives analytically
4. Use the first and second fundamental theorems of calculus to evaluate definite integrals and construct antiderivatives
   1. Fundamental theorem of calculus I for evaluating definite integrals
   2. Fundamental theorem of calculus II for constructing antiderivatives
   3. Fundamental theorem of calculus for evaluating improper integrals
5. Evaluate a definite integral as a limit
   1. Riemann sum
6. Apply integration to find area
   1. Signed area under a curve
7. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques
   1. Integration by substitution
   2. Integration by parts
   3. Integration by partial fraction expansion
   4. Integration using trigonometric substitutions
   5. Integrals of inverse functions
   6. Integrals of trigonometric, exponential and logarithmic functions
8. Apply integration to areas and volumes, and other applications, such as work or length of a curve
   1. Applications of integration to general problems from geometry involving areas, volumes and arc length
   2. Surfaces of revolution
   3. Volume of a solid of revolution
   4. Applications of definite integrals to problems from physics such as work, moments and centers of mass
   5. Applications of integrals to solve simple differential equations of motion
9. Evaluate improper integrals
   1. Find improper integrals
   2. Interpret improper integrals
10. Graph and differentiate functions in polar and parametric form
    1. Tangents to parametric and polar curves
11. Graph and integrate functions in polar and parametric forms
    1. Parametric curves
    2. Polar curves
12. Solve and interpret solutions to elementary differential equations
    1. Verification of solutions to elementary differential equations
    2. Use of slope fields to get qualitative information about solutions to differential equations
    3. Solutions to elementary first order differential equations by separation of variables
    4. Applications of differential equations to growth and decay problems
13. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (1) through (12) above
    1. Calculator/computer utilities for evaluating definite integrals
    2. Calculator/computer utilities for constructing graphs of antiderivatives
    3. Calculator/computer programs for approximating definite integrals
14. Discuss mathematical problems and write solutions in accurate mathematical language and notation
    1. Application problems from other disciplines
    2. Proper notation
15. Interpret mathematical solutions
    1. Explain the significance of solutions to application problems

Not applicable.

Written homework
Quizzes and tests
Proctored comprehensive final examination

Lecture
Discussion
Cooperative learning exercises

Briggs, W., L. Cochran, and B. Gillett. Calculus Early Transcendentals, 3rd ed.. 2018.

Alternative textbook: Calculus Volume 1, Openstax, 2021. https://openstax.org/details/books/calculus-volume-1

1. Homework problems covering subject matter from text and related material ranging from 30-60 problems per week. Students will need to employ critical thinking in order to complete assignments.
2. Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
3. Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems, write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system, such as Mathematica or MATLAB.
4. Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed inside and/or outside of class.