COURSE OUTLINE

For

CALCULUS I

(MTS–CAL–121)

Module Outline

1. Module code and Module title

Module code MTS–CAL–121

Module title Calculus I

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2. Module description

The aim of this module is to introduce to students the basic ideas of elementary calculus.

3. Learning outcomes

On completion of this module students will be able to:

(a) Differentiate functions.
(b) Apply the principles of differentiation to find rates of change and application.
(c) Integrate functions.
(d) Apply the principles of integration to solve engineering problems.

4. Module syllabus
Topic Contents/ fundamental concepts
(a) Differential Calculus • Limits and continuity
• Differentiation: Definition, from first principles,
differentiation of polynomial and trigonometric
functions, differentiation of inverse functions
• Rules of differentiation: Power, sum and difference,
constant multiple, product, quotient, chain and implicit
• Higher order derivatives
(b) Application of • Equations of tangents, normals and curve sketching.
Differential Calculus
• Applied maximum and minimum problems.
• Motion on a straight line.
• Related rates; differentials.

(c) The Integral • Definite and indefinite integrals of polynomials,

trigonometric functions and their combinations.
• Fundamental theorem of calculus
• Technique of integration: By table of integrals, by
substitution, by parts, by partial fractions decomposition.

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 (d) Application of • Calculation of area under a curve and area between two
Integration
curves by integration.
• Linear velocity, acceleration and displacement.
• Radioactive decay.
• Population growth.

5. Module components (Learning activities)

Lectures, tutorials, group work, assignments, self-study.

6. Assessment type
Assessment type Percentage
Test 1
15

Test 2
15

Test 3
20

Final Examination
50

7. Required and recommended readings

Required readings: • Lial, M. L., Hornby, J., & Schneider, D. I. (2020).
College algebra (7th ed). Pearson

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 • Joe, H., & Mourice, W. (2022). Thomas’ Calculus
early transcendentals (15th ed.). Pearson
• Stewart, J., Clegg, D. K., & Watson, S. (2020).
Calculus. Cengage Learning
• Ewer, J.P.G. (1994). Algebra, Trigonometry and
Calculus. STAM. Zomba. (JPGE)
Recommended readings: • Larson, R., & Edwards, B. H. (2022). Calculus of
a single variable (12th ed.) Cengage Learning
• Lial, M. L., Hornby, J., & Schneider. D.I. (2020).
College algebra and trigonometry (7th ed).
Pearson
• Swokowski, E.W., & Cole, J. A. (2018). Pre-
calculus: Functions and graphs (13th ed.). Brooks
Cole

8. Feedback for evaluation

The college through the Quality Assurance Directorate will administer students’ evaluation
questionnaire at the end of the module delivery.

9. Module schedule
Week Date(s) Topic/Activity Requirements
• Limits
01/07/24 • Properties of limits.
• Direct substitution property and
1 evaluation by replacement. Stewart J. & JPGE
• One-sided limits.
05/07/24 • Squeeze Theorem.

• Infinite limits and vertical

2 08/07/24 asymptotes. Stewart J. & JPGE
• Limits at infinity and horizontal
asymptotes.

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 • Infinite limits at infinity.
12/07/24 • Limits of trigonometric functions.
• Continuity.

Differentiation
15/07/24 • The derivative (differentiation from
first principles).
3 Stewart J. & JPGE
• Differentiation rules.
• Derivatives of trigonometric
19/07/24 functions.

TEST 1
22/07/24
• Chain rule.
• Implicit differentiation.
Class Notes
26/07/24 • Derivatives of inverse trigonometric
4 Stewart J. & JPGE
functions.
• Derivatives of exponential functions.
• Derivatives of logarithmic functions.
• Logarithmic differentiation.
• Higher order derivatives

Application of differentiation
29/07/24
• Tangents and normals.
5 • Maximum and minimum values
• Critical numbers and the closed Stewart J. & JPGE
02/08/24 interval theorem.

• First derivative test (increasing and

05/08/24 deceasing function).
• Second derivative test (concavity and
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inflection point).
Stewart J. & JPGE
• Curve sketching.
• Related rates.
09/08/24
• Differentials.

12/08/24
7 MID SEMESTER BREAK

16/08/24

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 • Optimization problems.
19/08/24 • Motion on a straight line.
Integration Stewart J. & JPGE
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• Antiderivatives.
• Indefinite integral.
23/08/24 • Standard integrals.
26/08/24 TEST 2
9 Class Notes
30/08/24
• Techniques of integration (reduction to
10 02/09/24 simple forms, integration by
substitution).
Stewart J. & JPGE
• Integration of trigonometric functions
06/09/24 • Integration of inverse trigonometric
functions.
• Integration of exponential functions.
11 09/09/24 • Integration of logarithmic functions.
• Integration by parts (reduction
Stewart J. & JPGE
formulae).
13/09/24 • Trigonometric integrals. Trigonometric
substitution.
• Partial fractions.
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16/09/24 • Quadratic expressions.
• Definite integrals. Stewart J. & JPGE
20/09/24 • Fundamental theorem of calculus.
• Definite integral and substitution.
• Area under the curve.

23/09/24 • Area between two curves.

Stewart J. & JPGE
13 • Linear velocity, acceleration and
displacement. Growth and decay
27/09/24
(radioactive decay and population
growth).
30/09/24
14 TEST 3
04/10/24

07/10/24
15 STUDY WEEK
11/10/24

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 14/10/24
16 SEMESTER 2 EXAMINATIONS
18/10/24

21/10/24
17 SEMESTER 2 EXAMINATIONS
25/10/24

10. Contact details for lecturer(s)

Lecturer's Name Dr. Solomon Kadaleka
Office Location WET BUILDING-Second Floor
Email skadaleka@mubas.ac.mw
Teaching Venue 404; 303; 307 & 43
Website www.mubas.ac.mw
Other information NA

11. Details of module website

NA

12 Academic honesty and plagiarism

Attention is drawn to University policy and regulations on honesty in academic work, and to the
disciplinary guidelines and procedures applicable to breaches of such policy and regulations.
Academic work submitted for assessment must be the original work of the author(s). If the ideas
or words of others have been drawn upon, this must be thoroughly and clearly acknowledged using
agreed scholarly conventions.