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Calculus I Course Outline

This document provides an overview of the Calculus I course, including: 1. The course covers limits, continuity, differentiation, integration, and their applications. 2. Assessment is based on continuous assessments tests (30%) and an end of semester exam (70%). 3. Topics include limits, differentiation techniques, applications of differentiation, antiderivatives, and calculating areas and volumes.

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818 views2 pages

Calculus I Course Outline

This document provides an overview of the Calculus I course, including: 1. The course covers limits, continuity, differentiation, integration, and their applications. 2. Assessment is based on continuous assessments tests (30%) and an end of semester exam (70%). 3. Topics include limits, differentiation techniques, applications of differentiation, antiderivatives, and calculating areas and volumes.

Uploaded by

MAGU_MWENYEWE
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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SMA 2101 Calculus I

Limits, continuity and differentiability. Differentiation by first principles and by rule for x n , integral and
fractional n, sums, products, quotients, chain rule, trigonometric, logarithmic and exponential functions of a
single variable. Parametric differentiation. Applications: equations of tangent and normal, kinematics, rates
of change and stationary points. Integration: anti-derivatives and their applications to areas and volumes.

Multimedia University of Kenya


Unit Code& SMA 2101: CALCULUS 1
Name
Prerequisite None
Cohort CITY2S2
Lecturer Marilyn Chepkurui Ronoh
Contact mcronoh1@gmail.com Mobile: 0727 878 308

Purpose
To enable student understand the simple concepts of the scientific method of analysis.

Learning Outcomes
By the end of this course unit the student should be able to do the following:-
1. Define and evaluate limits and continuity of functions
2. Differentiate functions of a single variable, Implicit and Parametric differentiation
3. Antiderivatives and application to areas and volumes

Teaching Methodologies
Lectures, practical sessions, group discussions and Tutorials.

Instructional Materials/Equipment
1. Whiteboard
2. Textbooks
3. Computers and Internet.

Course Assessment
Continuous Assessment Tests 30%
End of Semester Examination 70%

Course Content

WEEK TOPIC OUTLINE


WK1 I. Overview of the course Course outline and a brief overview of the course
II. Limits  Concept of a Limit
 Formal definition of a limit
WK 2 -
 Rules for calculating limits
5
 Methods for calculating limits
 Rationalization Method
 One sided limits
 The first remarkable limit
 Limits at infinity

WK 6 - Differentiation  Differentiation from first principles


12  Rules of differentiation
 Product rule
 Quotient rule
 Chain rule
 L’Hospital’s Rule
 Higher order derivatives
 Derivatives of trigonometric functions
 Implicit Differentiation
 CAT
 Differentiability theorem
 Logarithmic and Exponential differentiation
 Indeterminate forms of limits
 Parametric differentiation
 Applications

WK 12 Applications  Antiderivatives- Integration


- 14  Areas and Volumes

Reference Textbooks
1. Calculus and Analytic Geometry by G.B Thomas
2. An introduction to calculus by P.T Vas and J.H Were

Approved by: _______________________ Signature: ________________ Date: ____________

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