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7.2. Calculus I (Mandatory)

7.2.1. Justification ↑ Back to top

This course introduces the fundamental concepts of differential calculus of single-variable real functions. It provides the mathematical foundations necessary for analyzing change and motion in science and engineering, developing logical reasoning through the study of limits, continuity, and derivatives.

7.2.2. Generales Goals ↑ Back to top

1. Understand the fundamental concepts of limits and continuity.
2. Master differentiation techniques for algebraic and transcendental functions.
3. Apply derivatives to solve optimization problems and analyze rates of change.
4. Develop a rigorous approach to the formal definition of a derivative.

7.2.3. Contribution to Outcomes ↑ Back to top

ABET-1) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. (Familiarity)

7.2.4. Content ↑ Back to top

7.2.4.1. Limits and Continuity (20 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Stewart, 2016; Larson and Edwards, 2018; Thomas et al., 2014)

Topics

1. Limits and continuity of single-variable functions

Learning Outcomes

1. Interpret the concept of limit and continuity of a function and its relevance to modeling the behavior of engineering systems near a point [Familiarity]

7.2.4.2. Differential Calculus (20 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Stewart, 2016; Larson and Edwards, 2018; Thomas et al., 2014)

Topics

1. Derivatives and rules of differentiation

Learning Outcomes

1. Apply differentiation rules to find rates of change and optimize engineering design parameters [Usage]
2. Formulate and solve optimization problems for engineering systems using differential calculus [Assessment]

7.2.4.3. Integral Calculus (10 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Stewart, 2016; Larson and Edwards, 2018; Thomas et al., 2014)

Topics

1. The Fundamental Theorem of Calculus
2. Integration techniques including substitution and parts
3. Engineering applications of integration: areas, volumes, centroids, and moments of inertia

Learning Outcomes

1. State and explain the Fundamental Theorem of Calculus [Familiarity]
2. Calculate definite integrals arising from engineering problems such as work, fluid pressure, and heat transfer [Usage]

7.2.5. Bibliography ↑ Back to top

Stewart, J. (2016). Cálculo de una variable: Trascendentes tempranas. Cengage Learning, 8th edition.

Larson, R. and Edwards, B. H. (2018). Cálculo. Cengage Learning, 10th edition.

Thomas, G. B., Weir, M. D., and Hass, J. (2014). Cálculo de una variable. Pearson, 13th edition.