The document outlines a Calculus I course, including objectives, learning outcomes, weekly topics, textbooks, and assessment methods. The course aims to help students learn and apply calculus concepts like limits, continuity, derivatives, and integrals. Over 15 weeks students will cover functions, limits, derivatives, applications of derivatives, integrals, and techniques of integration. Assessment includes assignments, quizzes, midterms, and a final exam testing students' understanding of calculus concepts and their ability to apply calculus principles.

1. Department of Sciences & Humanities
FAST National University of Computer &
Emerging Science
CFD Campus
Course Outline
Course Code: MT 101
Course Title: Calculus-I
Credit Hours: 03
Contact Hours: 03
Prerequisite: None
Mode of Teaching: Three hours of lecture per week
Course Objectives
The primary aim of the course is to help students learn, understand, use and be able to explain
the ideas of calculus. In addition, it is desired that students will improve their mathematical
skills, further their understanding of mathematics and its applications and increase both their
intellectual curiosity and their desire to learn more about the value of mathematics in general
and calculus in particular.
Course Learning Outcomes (CLOs)
Upon successful completion of the course, the student will demonstrate competency by being
able to:
1. State a precise intuitive definition of the limit of a function.
2. Evaluate limits of functions using numerical, graphical and algebraic methods.
3. State a precise intuitive definition of the continuity of a function.
4. Understand, explain, and use average rate of change and instantaneous rate of
change.
a. State the definition of the derivative of a function as the limit of a difference
quotient.
b. Use the limit of difference quotient definition of derivative to find simple
derivatives.
c. Find the derivative of any elementary function (algebraic, logarithmic or
exponential) or combination thereof.
d. Find higher order derivatives.
e. Find the slope of the graph of a function.
f. Find the tangent line to the graph of a function.
g. Find relative extrema and points of inflection of a function.
h. Use derivative information to describe the graph of a function.
i. Determine relative and absolute extrema of a function.
j. Solve problems involving rectilinear motion, velocity and acceleration.
5. Use L'Hospital's Rule to determine indeterminate limits.

2. Department of Sciences & Humanities
FAST National University of Computer &
Emerging Science
CFD Campus
Course Outline
6. Write and apply the definition of an indefinite integral.
a. Determine general antiderivatives using basic integration formulas and rules.
b. Use an initial condition to find a particular solution to an integral equation.
c. Write and apply the definition of a definite integral.
d. State and apply the fundamental theorem of calculus.
e. Use recognition, substitution, and integration by parts to evaluate both
definite and indefinite integrals.
Weekly Schedule
Topic CLO PLO Assessm
ent
Methodo
logy
Learning
Domain
Level of
Learning
1 Functions
1. W Ways to represent a function,
2. New functions from old,
3. F Families of functions, Inverse functions,
Inverse trigonometric functions,
Exponential and Logarithmic functions,
Parametric equations.
1
2 Limits
4. L Limits (An intuitive approach),
5. Computing limits.
6.
2
3 Limits
7. L Limits at infinity,
8. End behavior of a function.
9.
2
4 Continuity
10. C Continuity of trigonometric and inverse
11. functions.
12.
3
5 Derivatives
Tangent Lines, Velocity, and General
Rates of Change, The Derivative
Function, Techniques of Differentiation,
The Product and Quotient Rules,
Derivative of Trigonometric Functions,
The Chain Rule, Related Rates, Local
Linear Approximation; Differentials.
4

3. Department of Sciences & Humanities
FAST National University of Computer &
Emerging Science
CFD Campus
Course Outline
6 Inverse/Transcendental functions
13. I Implicit Differentiation.
14.
4
7 Inverse/Transcendental functions
D Derivatives of Logarithmic Functions,
D Derivatives of Exponentials and Inverse
Functions.
4
8 Indeterminate forms
L'Hospital's Rule; Indterminate Forms.
5
9 Applications of derivatives
15. A Increase, Decrease, and Concavity, Relative
16. Extrema, Graphing Polynomials,
17. Curves with Cusps and Vertical Tangent
18. Lines.
19.
4
1
0
Applications of derivatives
20. A Absolute Maxima's and Minima,
21. Applied Maximum and Minimum Problms,
22. Rolle's Theorm; Mean Value Theoem,
23. Rectilinear Motion.
24.
25.
4
1
1
Definite integrals
26. A An overview of the area Problem,
27. The Indefinite Integral,
28. In Integration by Substitution.
29.
6
1
2
Definite integrals
30. DDefinition of Area as a limit; Sigma Notation,
31. ThThe Definite Integral, The Fundamental
32. Theorem of Calculus.
33.
6
1
3
Applications of integrals
Area Between Two Curves,
Volumes by Slicing; Disks and Washers.
6
1
4
Applications of integrals
Length of a Plane Curve.
6
1
5
Techniques of integration
34. A An overview of Integration Methods.
35. In Integration by Parts.
6
1 Improper Integrals 6

4. Department of Sciences & Humanities
FAST National University of Computer &
Emerging Science
CFD Campus
Course Outline
6
Books
Text Book(s)
Title Thomas’ Calculus 11th
/12th
edition
Author Thomas and Finney
Ref. Book(s)
Title Calculus
Author James Stewart
Assessment System
Assignments 05%
Quizzes 10%
Mid Terms (I+II) 35%
Final Term 50%
Assessment of Course Learning Objectives
Assignments
Labs
Quizzes
OHT-1
OHT-2
Viva
Presentation
Individual
Project
Group
Project
Class
Participation
FinalExam
CLOs     