General Mathematics

Teacher

Sasmita Jena

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Core Courses

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Course Name :General Mathematics

Code(Credit) : CUTM1250(2-1-0)

Course Objectives

To determine the quadrants where sine, cosine and tangents are positive and negative.
Using the fundamental identities of trigonometry.
Evaluate inverse functions.
Know event, outcome, trial, simple event, sample space and calculate probability of an event will occur.
To make an inference about a population of interest based on information.
To examine a limit exists or doesn’t exists at a point.
Find the rate of change in velocity and acceleration.
Use of different relations of derivatives of a function.
Area under the graph of a non-negative function.

Learning Outcomes

Use of various methods to compute the probabilities of events.
Organize, present and interpret statistical data ,both numerically and graphically.
Uniqueness of limit, fundamental theorem on limits, trigonometric limits, exponential limits, logarithm limits.
Instantaneous rate of change of a quantity with respect to others.
Area, Volume, Displacement of functions under the graph.

Course Syllabus

Module I – Trigonometry (T)(06 hrs)

Sum and difference of two angles sin(A±B),cos(A±B),tan(A±B), Multiple angles: sin2A,cos2A,tan2A,sin3A,cos3A,tan3A, Sine formula, solving problems, Cosine formula, solving problems, Inverse trigonometry: Definition of inverse trigonometric functions, relation between the inverse trigonometric functions.

Practice(3hrs)

Module II – Limits (T)(04 hrs)

Definition of limit, methods of evaluating limit(finite & infinite limits), Algebra limit: limit of sum, difference, product and quotient of two functions, solving problems, R.H.L, L.H.L, existence of limit, solving problems, Standard formulas of limit.
(i)lim┬(x→0)⁡〖sinX/x=1〗 (ii)lim┬(x→0)⁡〖tanX/x=1〗
(iii)lim┬(x→0)⁡〖(a^x-1)/x=log_e⁡a 〗 (iv)lim┬(x→0)⁡〖(e^x-1)/x=1〗 ,
(V)lim┬(x→a)⁡〖(x^n-a^n)/(x-a)=na^(n-1) 〗
Solving problems.

Module III – Differentiation (T)(06 hrs)

Definition of differentiation, formula for algebraic, trigonometric, exponential and logarithmic functions, solving problems and differentiation, Algebra of differentiation: formula for sum, difference, product, quotient of two functions, Chain rule [differentiation of function of function], Differentiation of inverse trigonometric functions, implicit functions, solving problem functions, Successive differentiation: successive differentiation of functions upto 2nd order, Partial differentiation: definition of partial differentiation, partial differentiation of two variables upto 2nd order, solving problems.

Practice(3hrs)

Module IV – Integration (T)(05 hrs)

Definition of integration, showing standard formulas of integration by the reverse process of differentiation, solving problems using decomposition method, Integration by method of substitution, integrals of the following forms,
(i)∫▒F[f(x)]f'(x)dx (ii)∫▒〖f'(x)/f(x) dx〗 (iii)∫▒〖[f(x)]^n f'(x)dx〗
Integration by parts: integrals of the following forms,
(i)∫▒〖X sinxXdx〗 (ii)∫▒〖X cosXdx〗 (iii)∫▒〖x^n log⁡Xdx 〗 (iv)∫▒〖x e^nx dx〗, solving problems.
Definite integration: definition of definite integration, properties of definite integration, solving problems, Area function: definition of area function, finding area bounded by the curves, solving problems.

Practice(3hrs)

Module V – Probability (T)(02 hrs)

Definition of random experiment, outcome, sample space, simple problems, Event, occurrence of an event, probability of an event, solving problems.

Practice(3hrs)

Module VI – Statistics (T)(02 hrs)

Definition of mean, median, mode, formula for mean, median, mode, simple problems, Variance and standard deviations: variance, standard deviation of ungrouped and grouped data, simple problems.

Practice(3hrs)

 

Reference Books:-    

  • Elements of mathematics Vol. I and II
  • Mathematics book by R.D. Sharma for class XI & XII
  • Higher secondary mathematics for class XI & XII
  • NCERT book for class XI & XII

Session Plan

Session 1

Sum and difference of two angles

LECTURE: Discuss about the sum and difference between angles, sin(A±B),cos(A±B),tan(A±B)

Sum & Difference of two angles

Session 2

Multiple angles

LECTURE: Discuss about various types of multiple angles like: sin2A,cos2A,tan2A,sin3A,cos3A,tan3A

Multiple Angles

Session 3

Sine formula

LECTURE: Discuss about all types of Sine formulas, solving problems.

Sine Formula

Session 4

Cosine formula

LECTURE: Discuss about all types of Cosine formulas, solving problems.

Cosine Formula

Session 5

Inverse trigonometry

LECTURE: Definition of inverse trigonometric functions, relation between the inverse trigonometric functions.

Inverse Trigonometry

Session 6 , 7 & 8

Practice
Use of Mathematical Operators in spreadsheet.
Use of Mathematical operators

Session 9

Limits

LECTURE: Definition of limit, methods of evaluating limit(finite & infinite limits).

Introduction to Limits

Session 10

Algebra limit

LECTURE: Discuss about limit of sum, difference, product and quotient of two functions, solving problems.

Algebra Limit

Session 11

R.H.L & L.H.L

LECTURE: Explain Limit of a function, R.H. Limit, L.H. Limit & existence of Limits.

About R.H.L & L.H.L.

Session 12

Standard formulas of limit

LECTURE: Methods of evaluating Limit (Finite & Infinite Limits) and discuss about all Standard formulas of Limit

Standard Formulas of limit

Session 13

Differentiation

LECTURE: Definition of differentiation, formula for algebraic, trigomometric, exponential and logarithmic functions, solving problems and differentiation.

Introduction to Differentiation

Session 14

Algebra of differentiation

LECTURE: Discuss about formula for sum, difference, product, quotient of two functions.

Algebra of Differentiation

Session 15

Chain rule

LECTURE: Discuss about to Perform derivative of composite function(chain rule), problems on chain rule.

Introduction To Chain Rule

Session 16

Differentiation of inverse trigonometric functions

LECTURE: Discuss about Differentiation of inverse trigonometric functions, implicit functions, solving problem functions.

Differentiation of Inverse Trigonometry

Session 17

Successive differentiation

LECTURE: Discuss about successive differentiation of functions upto 2nd order.

WEBLINKS:

Session 18

Partial Differentiation

LECTURE: definition of partial differentiation, partial differentiation of two variables upto 2nd order, solving problems.

Introduction to Partial Differentiation

Session 19

, 20 & 21

Practice
Use of Mathematical Functions in a spreadsheet.
Use of Mathematical functions

Session 22

Integration

LECTURE: Definition of integration, showing standard formulas of integration by the reverse process of differentiation, solving problems using decomposition method.

Introduction to Integration

Session 23

Integration by subtitution method

LECTURE: Discuss about Integration by method of substitution, integrals of the following forms.

Integration By Substitution Method

Session 24

Integration by parts

LECTURE: Discuss about Integration by parts: integrals of the following forms

Integration by parts

Session 25

Definite integration

LECTURE: definition of definite integration, properties of definite integration, solving problems.

Definite Integration

Session 26

Area function

LECTURE: definition of area function, finding area bounded by the curves, solving problems.

Area Function

Session 27

, 28 & 29

Use of Logical Functions in a Spreadsheet.
Use of Logical Functions

Session 30

Probability

LECTURE: Definition of random experiment, outcome, sample space, simple problems

Introduction To Probability

Session 31

Event

LECTURE: What is an event, occurrence of an event, probability of an event, solving problems.

Introduction To Event

Session 32

, 33 & 34

Practice
Unit Conversion
Unit Conversion

Session 35

Statistics

LECTURE: Definition of mean, median, mode, formula for mean, median, mode, simple problems.

Introduction To Statistics

Session 36

Variance and standard deviations

LECTURE: Discuss about variance, standard deviation of ungrouped and grouped data, simple problems.

Variance and Standard Deviations

Session 37

, 38

,39

Practice
Conversion between Imperial & Metric Systems.
Conversion between Imperial and Metric System

Evaluation of Formulae.
Evaluation of Formulae

Case Studies

Case Studies

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