Foundations of Single Variable Calculus

COURSE DESCRIPTION

Learn to perform differentiation, optimization, and integration like you have never seen before. Students will learn calculus by analyzing case studies, participating in round tables, conducting research, and with many more tools.

 

COURSE PRE-REQUISITES

Introduction to Calculus: concepts such as factorization, functions, equation-solving techniques, and graph interpretation of functions are required to take Calculus of Functions in One Variable I effectively.

 

CONTENT

Unit I. Limits and Continuity

o Limit concept.

o Limit technique.

o Infinity and limits.

o Properties of continuity and types of discontinuity.

Unit II. Derivatives

o Derivative concept.

o Differentiation rules.

o Derivatives of products, quotients, trigonometric functions, logarithms,

exponentials, and inverse functions.

o Rate of change.

o Chain rule.

o Implicit differentiation.

o Extrema, mean value theorem.

o Graph analysis.

o Optimization.

o L’Hopital Rule.

Unit III. Integrals

o Anti-derivative.

o Areas under curve.

o Definite integral.

o Fundamental Theorem of Calculus.

o Integral techniques

 

ASSIGNMENTS

PERCENTAGE VALUE

Oral presentations to present the results of the case studies (3 in total): 20 %

Round tables (3 in total): 10 %

Written reports (3 in total): 30 %

Mind maps (12 in total): 20 %

Final assignment (1 in total) 20 %

Total 100%