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Calculus I

This course will introduce students to the different applications of both differential and integral calculus. Major topics covered in differential calculus include optimization and marginal analysis problems for single and multi-independent variable models, as well as applications of the first and second derivatives. Major topics covered in integral calculus include the notion of an anti-derivative, indefinite and definite integrals, and procedures for finding either area under one curve or between two curves.

Topics Included:

  • Review of Math Principles and College Algebra
  • Functions, Limits, and Derivatives
  • Differentiation
  • Applications of Derivatives
  • Logarithmic Functions
  • Integration
  • Calculus of Several Variables

Course Benefits & Learning Outcomes:

  • Take first derivatives of single independent variable functions using the power, product, quotient, and chain rules.
  • Take second derivatives of single independent variable functions to assist in determining relative maximum and minimum values and inflection points.
  • Take partial derivatives of multiple independent variable functions.
  • Use first and second derivatives to solve characteristics optimization and “Rate of Change” application problems for single and multiple independent variable functions.
  • Relate the process of anti-differentiation to the process of differentiation; take anti-derivatives of the most common functions found in an applied environment.
  • Relate anti-derivatives and indefinite integrals.
  • Understand the fundamental theorem of calculus, and its implications for applied business problems.
  • Relate the definite integral and applications problems requiring knowledge of the area under a curve and how to find the area between two curves.

Transferring UC San Diego Division of Extended Studies Credit

Many UC San Diego Division of Extended Studies may qualify for college credit to UC San Diego or other colleges or universities. The transfer of credit is determined solely by the receiving institution. You should discuss how your individual courses will transfer with the registrar's office at the receiving institution before you enroll.

Course typically offered: Online every quarter. Lectures are pre-recorded and can be watched during the week at the students' convenience. Live discussion sessions will be held Thursdays from 9am to 10am PST. Exams will be given online during a set date and time.

Prerequisites: Knowledge of college Algebra.

Next steps: Upon completion, consider enrolling in MATH-40019: Calculus II or other Applied Mathematics coursework for continued learning.

More information: For more information about this course, please contact

Course Number: MATH-40024
Credit: 4.00 unit(s)

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