Course Outline for Mathematics 1
Calculus I

Effective: Fall 2022
SLO Rev: 10/26/2021

Catalog Description:

MTH 1 - Calculus I

5.00 Units

This course is the first in the three-course calculus sequence intended for majors in math, engineering, and physical sciences. The course covers elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and trigonometric functions, and the definite integral. Application to the sciences are also covered.
Prerequisite: MTH 20 or MTH 22 or MTH 21 and MTH 36 or MTH 21 and MTH 37 an appropriate skill level demonstrated through the mathematics assessment process.
CB03: TOP Code 1701.00 - Mathematics, General
Course Grading: Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 5.00 90.00 180.00 270.00
Total 5.00 90.00 180.00 270.00

Measurable Objectives:

Upon completion of this course, the student should be able to:
  1. use delta notation;
  2. explain limits and continuity;
  3. find the limit of a function at a real number;
  4. determine if a function is continuous at a real number;
  5. use Newton’s method;
  6. apply the definition of the derivative of a function;
  7. find the equation of a tangent line to a curve;
  8. define velocity and acceleration in terms of mathematics;
  9. differentiate algebraic and trigonometric functions using differentiation formulas;
  10. find all maxima, minima, and points of inflection on an interval;
  11. sketch the graph of a differentiable function;
  12. use differentiation to solve optimization problems;
  13. apply implicit differentiation to solve related rate problems;
  14. apply the Mean Value Theorem;
  15. find the value of a definite integral as the limit of a Riemann sum;
  16. integrate a definite integral using the Fundamental Theorem of Integral Calculus;
  17. find areas using the definite integral;
  18. find differentials and use differentials to solve applications;
  19. differentiate appropriate functions using the Fundamental Theorem of Integral Calculus;
  20. find the volume of a solid of revolution using the shell, disc, washer methods;
  21. integrate using the substitution method;
  22. find the volume of a solid by slicing;
  23. determine the average value of a function.

Course Content:

  1. Review relations, functions and graphs
  2. Review lines, equations and slopes
  3. Limits and continuity using graphical, numerical and algebraic approaches
  4. Definition of a derivative as a limit
  5. Mean Value Theorem
  6. Interpretation of a derivative
    1. Slope of a tangent line
    2. Rate of change
  7. Differentials and their applications
  8. Differentiation of algebraic functions
  9. Differentiation of trigonometric functions
  10. Differentiation rules including the chain rule
  11. Implicit differentiation
  12. Differeniation of inverse functions
  13. Higer order derivatives
  14. Maxima, minima and points of inflection
  15. Curve sketching
  16. Applications of differentiation
    1. Related rates
    2. Optimization
  17. Newton’s Method
  18. Antiderivatives
  19. Riemann sum
  20. Definite integral and the Fundamental Theorem of Integral Calculus
  21. Mean Value Theorem for Definite Integrals
  22. Average value of a function
  23. Integration by substitution
  24. Areas of plane regions
  25. Volume of solids of revolutions
  26. Volume of solid by slicing

Methods of Instruction:

  1. Audio-visual materials
  2. Lecture/Discussion
  3. Group Activities
  4. Problem Solving
  5. Textbook reading assignments
  6. Distance Education

Assignments and Methods of Evaluating Student Progress:

1. Typical Assignments
  1. Show, using implicit differentiation, that any tangent line at a point P to a circle with center O is perpendicular to the radius OP.
  2. Find the equation of the line tangent to the graph of f(x) =sin(x) at x = pi/2.
  3. Find the volume generated by revolving a disc of radius 1 unit around an axis that is 2 units away from the center of the disc and parallel to a diameter of the disc.
2. Methods of Evaluating Student Progress
  1. Exams/Tests
  2. Quizzes
  3. Home Work
  4. Class Work
  5. Final Examination
3. Student Learning Outcomes
Upon the completion of this course, the student should be able to:
  1. critically analyze mathematical problems using a logical methodology;
  2. communicate mathematical ideas, understand definitions, and interpret concepts;
  3. increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.

Textbooks (Typical):

  1. Briggs, W., L. Cochran, B. Gillett. E. Schulz (2019). Calculus (3rd). Pearson.
Additional Materials:
  • A scientific or graphing calculator may be required.
  • Access code to a software learning system may be required.

Abbreviated Class Schedule Description:

Elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and trigonometric functions, the definite integral.
Prerequisite: MTH 20 or MTH 22 or MTH 21 and MTH 36 or MTH 21 and MTH 37 an appropriate skill level demonstrated through the mathematics assessment process.