  
Description  
 Introduction to integral calculus including definite and indefinite integrals, the first and second Fundamental Theorems and their applications to geometry, physics, and the solution of elementary differential equations.


Course Objectives  
 The student will be able to:
 Demonstrate an understanding of and evaluate and approximate definite integrals.
 Find antiderivatives graphically, and analytically.
 Use the First and second Fundamental Theorems of calculus to evaluate definite integrals and construct antiderivatives.
 Evaluate a definite integral as a limit.
 Apply integration to find area.
 Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
 Apply integration to areas and volumes, and other applications such as work or length of a curve.
 Evaluate improper integrals.
 Graph and integrate functions in polar and parametric forms.
 Solve and interpret solutions to elementary differential equations.
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (J) above.
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Interpret mathematical solutions.

Special Facilities and/or Equipment  
 A.Graphing Calculator. When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Demonstrate an understanding of and evaluate and approximate definite integrals.
 Signed Area under a curve and the net change of a function F from f
 Properties of integrals
 Approximating definite integrals
 Interpretations of the definite integral
 Average value of a function
 Numerical approximations to definite integrals using Rectangular, Trapezoidal and Simpson's approximation and estimation of errors
 Find antiderivatives graphically, and analytically.
 The graphical relationship between a function and its antiderivatives
 Construction of antiderivatives analytically
 Use the First and Second Fundamental Theorems of calculus to evaluate definite integrals and construct antiderivatives.
 Fundamental theorem of calculus I for evaluating definite integrals
 Fundamental theorem of calculus II for constructing antiderivatives
 Fundamental Theorem of calculus for evaluating improper Integrals
 Evaluate a definite integral as a limit.
 Riemann Sum
 Apply integration to find area.
 Signed area under a curve
 Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
 Integration by Substitution
 Integration by Parts
 Integration by Partial Fraction Expansion
 Integration using Trigonometric Substitutions
 Integrals of inverse functions
 Integrals of trigonometric, exponential and logarithmic functions
 Apply integration to areas and volumes, and other applications such as work or length of a curve.
 Applications of integration to general problems from geometry involving areas, volumes and arc length
 Surfaces of revolution
 Applications of definite integrals to problems from physics such as work, moments and centers of mass
 Applications of integrals to solve simple differential equations of motion
 Evaluate improper integrals.
 Find improper integrals
 Interpret improper integrals
 Graph and integrate functions in polar and parametric forms.
 Parametric Curves
 Polar Curves
 Solve and interpret solutions to elementary differential equations.
 Verification of solutions to elementary differential equations
 Use of slope fields to get qualitative information about solutions to differential equations
 Solutions to elementary first order differential equations by separation of variables
 Applications of differential equations to growth and decay problems
 Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (J) above.
 Calculator/computer utilities for evaluating definite integrals
 Calculator/computer utilities for constructing graphs of antiderivatives
 Calculator/computer programs for approximating definite integrals
 Discuss mathematical problems and write solutions in accurate mathematical language and notation.
 Application problems from other disciplines
 Proper notation
 Interpret mathematical solutions.
 Explain the significance of solutions to application problems

Methods of Evaluation  
  Written homework
 Quizzes & tests
 Proctored comprehensive final examination

Representative Text(s)  
 Briggs W., L. Cochran, and B. Gillett, Calculus Early Transcendentals, 2nd ed. Boston, Pearson, 2015.

Disciplines  
 Mathematics


Method of Instruction  
 Lecture, Discussion, Cooperative learning exercises.


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: 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.
 Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
 Projects: 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.
 Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.
