### Calculus-I(MATH-5101)

Introduction: Calculus is the branch of mathematics that deals with the finding and properties of derivatives and integrals of function, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus. This is the first course of the sequence, Calculus-I, II and III, serving as the foundation of advanced subjects in all areas of mathematics. The sequence, equally, emphasizes basic concepts and skills needed for mathematical manipulation. Calculus I and II focus on the study of functions of a single variable.

Prerequisite(s): None

Description and Objectives of the course

Calculus is the mathematical study of continuous change .If quantities are continually changing ,we need calculus to study what is going on .Calculus is concerned with comparing quantities which vary in a non-linear way. It is used extensively in science and engineering,since many of the things we are studying(like velocity, acceleration ,current in a circuit)  do not behave in asimple, linear  fashion. Calculushas two major branches,differential calculus(Calculus -I) and integral calculus (Calculus -II); the former concerns instantaneous  rate of change, and the slopes of the curves, while integral calculus concernsaccumulation of quantities, and area under or between curves. This is the first course of sequence ,Calculus-I, II and III, serving as the foundation of advanced subjects in all ares of mathematics.The sequence ,equally, emphasizes basicconcepts and skills needed for mathematical manipulation. It focus on the study of functions of a single variable.Calculus-I is an introduction to differential and integral calculus:the study of change.

Intended learing outcomes

After successful completion of this course,

1. Students will be able to solve algebraic equations and inequalities involving the square root and modulus function, they recognize odd, even, periodic, increasing,and decreasing functions
2. They will be able to recognize linear, quadratic, power, polynomial, algebraic, rational, trigonometric, exponential, hyperbolic and logarithmic functions and sketch their graphs.
3.  They will be able to calculate limits by substitution and by eliminating zero, calculate limits at infinity of rational functions and calculate limits in indeterminate forms by a repeated use of l’Hˆopital’s rule.
4. know the basic rules of differentiation and use them to find derivatives of products and quotients, know the chain rule and use it to find derivatives of composite function.
5.  They will be able to use derivatives to find intervals on which the given function is increasing or decreasing.
6. Understand the concept of definite integral and know the basic properties of definite integrals.
7. Now the fundamental theorem of calculus and be able to use it for evaluating definite integrals and derivatives of integrals with variable limits of integration

Course Contents

1.  Functions and their graphs, Rates of change and tangents to curves.
2. Limit of a function and limit laws, The precise definition of a limit.
3. One-sided limits ,continuity,limits involving infinity:asymptotes of graphs.
4. Differentiation: tangent and derivative at apoint, the derivative as a function.
5. Differentiation rules, the derivative as a rate of change .
6. Derivative of trignometric functions, chain rule, implicit differentiation.
7. Related rates,linearization and differentials, higher derivatives.
8. Applications of derivatives: extreme values of functions.
9.  Rolle's theorem, the mean value theorem, Monotonic functions and the first derivative test.
10.  Concavity and curve sketching.Applied optimization, Antiderivatives,integration:area and estimating with finite sums
11. Applied optimization, Antiderivatives,integration:area and estimating with finite sums.
12. Definite integral, the fundamental theorem of calculus. Indefinite integral.
13. Applications of definite integrals :volume using cross-sections.
14. Volumes using cylinderical shells, arc length,Areas of surfacesof revolution.
15.  Transdental functions: Cauchy’s residue theorem with applications.
16. Exponential functions,indeterminate forms and L' Hopital's rule,Inverse trignometric functions,hyperbolic functio

Recommended Books

1. Stewart, J. (2015). Calculus (8th ed.) . Boston :Cengage Learning.
2.  Thomas , G. B., Weir, M.D. and Hass, J. R. (2014) Thomas' Calculus: single variable (13th ed.). London:Pearson plc.

Suggested Books

1. Anton. H., Bivens I. C. and Davis, S.(2016). Calculus (11th ed.). New York: Wiley.
2. Larson, R. and Edwards,B.H.(2013). Calculus( 10th ed.). New York :Brooks Cole.

### Assessment  Criteria

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

### Key Dates and Time of Class Meeting

Thursday                                                                                 12:30 pm-02:00 pm

Friday                                                                                       11:00 am-12:30 am

Commencement of Classes                                                   October 26, 2020

Mid Term Examination                                                            December 28, 2020

Final Term Examination                                                          March 1 - 5, 2020

Declaration of Result                                                              March 12, 2020