Course goals and learning outcomes support the Foundational Component Areas defined by the Texas Higher Education Coordinating Board. Course goals are linked to the respective Core Curriculum Competencies: Critical Thinking Skills, Communication Skills, and Empirical and Quantitative Skills. Specific competencies are identified in designated course goals and learning outcomes.

Upon successful completion of this course, students will:

Develop solutions for tangent and area problems using the concepts of limits, derivatives, and integrals by
1. identifying limits graphically;
2. determining limits numerically;
3. evaluating limits analytically;
4. evaluating one sided limits;
5. evaluating limits at infinity;
6. evaluating limits using L’Hopital’s Rule;
7. defining the derivative of a function;
8. using the definition to find the derivative of a function;
9. writing the equation of a tangent line to the graph of a function at a given point;
10. defining, calculating, and applying the differential;
11. applying basic anti-differentiation rules to evaluate indefinite integrals for algebraic, trigonometric, logarithmic, exponential, inverse trigonometric, and hyperbolic functions;
12. using a u-substitution to integrate;
13. evaluating the area of a bounded region using the definite integral.
Draw graphs of algebraic and transcendental functions, considering limits, continuity, and differentiability at a point by
1. defining a critical number of a function;
2. using critical numbers to identify relative extrema;
3. using the first derivative to identify the intervals on which a function is increasing or decreasing;
4. applying the First Derivative Test to locate extrema;
5. using the second derivative to identify the intervals on which a function is concave up or concave down to find the inflection points;
6. applying the Second Derivative Test to locate extrema;
7. applying Rolle’s Theorem and the Mean Value Theorem.
Determine whether a function is continuous and/or differentiable at a point using limits by
1. defining continuity at a point;
2. defining continuity on an open interval;
3. defining continuity on a closed interval;
4. identifying any discontinuity of a function;
5. defining differentiability at a point.
Use differentiation rules to differentiate algebraic and transcendental functions by
1. applying basic differentiation rules for algebraic, trigonometric, logarithmic, exponential, inverse trigonometric, and hyperbolic functions;
2. using differentiation rules to find higher order derivatives;
3. using implicit differentiation to differentiate with respect to a given variable;
4. differentiating functions defined by integrals.
Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems by
1. applying implicit differentiation to solve related rate problems;
2. solving optimization problems using extrema.
Evaluate definite integrals using the Fundamental Theorem of Calculus by
1. using the limit of a Riemann sum to evaluate a definite integral;
2. using the Fundamental Theorem of Calculus to calculate a definite integral.
Articulate the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.
Demonstrate lab skills by
1. analyzing the limit of a function;
2. examining the continuity of a function;
3. investigating the derivative of a function;
4. examining applications of differentiation;
5. investigating the indefinite integral of a function;
6. analyzing the definite integral of a function.
Critical Thinking Skills: Demonstrate the ability to evaluate, synthesize, and perform inquiry and analysis of information in mathematical problems by
1. applying implicit differentiation to solve related rate problems;
2. solving optimization problems using extrema.
Communication Skills: Demonstrate the ability to communicate orally, visually, and/or in writing using mathematical language and symbols by
1. analyzing and interpreting graphs;
2. illustrating the solution steps for optimization problems.
Empirical and Quantitative Skills: Manipulate and analyze numerical data or observable facts in making informed conclusions by
1. evaluating area under a curve using techniques of integration;
2. utilizing the derivative as a rate of change.

MATH 2413

Download as PDF

MATH 2413 - Calculus I