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5.10. Integral Calculus (Mandatory)

5.10.1. Justification ↑ Back to top

Integral calculus is a fundamental mathematical tool shared by computer science and engineering disciplines, essential for modeling and solving problems involving accumulation, change, and areas under curves. This course provides the foundations of integral calculus, including integration techniques and their applications in scientific and engineering contexts.

5.10.2. Generales Goals ↑ Back to top

1. Understand the concept of definite and indefinite integrals.
2. Apply various integration techniques to solve problems.
3. Use integral calculus to model and solve problems in scientific and engineering contexts.

5.10.3. Contribution to Outcomes ↑ Back to top

AG-C07) Computing Knowledge: Applies knowledge of mathematics, science, and computing. (Familiarity)

5.10.4. Content ↑ Back to top

5.10.4.1. Antiderivatives and Integration Techniques (20 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Stewart, 2015; Larson and Edwards, 2014)

Topics

1. The Fundamental Theorem of Calculus and the antiderivative
2. Integration techniques: substitution, parts, partial fractions, and trigonometric substitution

Learning Outcomes

1. State the Fundamental Theorem of Calculus and explain the relationship between differentiation and integration [Familiarity]
2. Compute definite and indefinite integrals using standard techniques including substitution and integration by parts [Usage]

5.10.4.2. Improper Integrals (8 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Stewart, 2015; Larson and Edwards, 2014)

Topics

1. Improper integrals: convergence criteria and comparison tests

Learning Outcomes

1. Determine convergence of improper integrals using comparison and other convergence tests [Assessment]

5.10.4.3. Sequences, Series, and Power Series (20 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Stewart, 2015; Larson and Edwards, 2014)

Topics

1. Sequences and series: convergence tests (ratio, root, comparison, integral)
2. Power series, radius of convergence, Taylor and Maclaurin series

Learning Outcomes

1. Determine convergence of power series and construct Taylor series for standard functions [Assessment]

5.10.5. Bibliography ↑ Back to top

Stewart, J. (2015). Calculus: Early Transcendentals. Cengage Learning.

Larson, R. and Edwards, B. H. (2014). Calculus. Cengage Learning.