This course is designed to develop the topics of Equations and differential calculus. At the end of this course and following completion of an appropriate amount of independent study, students will be able to apply basic principles of Algebra and differentiation techniques in their respective disciplines.
Elementary Concepts: Real numbers and subsets of real numbers, real line, BODMAS, Equations and their solutions: Quadratic equations and their solutions by factorization, completing squares and quadratic formula, Exponential and Logarithmic functions Matrices and Determinants: Matrix Algebra of matrices, determinants, expansion of determinants, Cramer’s Rule, Two dimensional coordinate system and graphs, Differentiation: Basic formulas of differentiations, theorems on differentiation (sum, difference, product and quotient rules without derivations), Chain rule, derivative of six basic trigonometric functions, Integration: Formulas of integration, theorem of integration (sum, difference, exponent and logarithms without derivations), integration by substitution, integration by parts (simple applications).
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Theory: |
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Lectures |
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Class Participation |
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Assignments |
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Quiz’s |
Goal 1: Student should be able to understand the basics of Mathematics
Objective 1: Introduction to Mathematics
Objective 2: Basic Notations of Mathematics
Objective 3: Elementary concept of real number systems
Goal 2: Student should be able to understand the fundamental concept of Equations
Objective 1: Concept of Polynomials
Objective 2: Concept of Linear Equations
Objective 3: Concept of Quadratic Equations
Goal 3: Student should be able to understand the Concept of Exponential and Logarithmic functions
Objective 1:Exponential functions
Objective 2:Logarithmic functions and Scales
Objective 3:Exponential growth and decay
Goal 4: Student should be able to understand the concept of Matrices
Objective 1: Definitions of Matrices
Objective 2: Concept of Matrix Algebra
Objective 3: Concept of Determinants
Goal 5: Student should be able to understand the concept of Differentiation
Objective 1: Concept of Rate of Change
Objective 2: Basic idea of Secant and Tangent line
Objective 3: Different Rules to find the derivatives
Goal 6: Student should be able to understand the concept of Integration.
Objective 1: Concept of Area under the curve
Objective 2: Different rules to find the integration
Objective 3: Concept of Integration by Parts
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Theory
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Modality
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Assignment |
Mid Term |
Final Term |
Total |
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Max marks |
4 |
12 |
24 |
40 |
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No |
Theory |
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1 |
Preliminary concepts of Algebra |
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2 |
Sets and Real Number systems |
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3 |
Concept of Polynomials |
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4 |
Concept of Equations |
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5 |
Linear and Absolute value equation |
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6 |
Linear equation and their solutions |
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7 |
Quadratic equations |
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8 |
Solutions of Quadratic equations |
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9 |
Exponential Functions and their Applications in Life sciences |
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10 |
Logarithmic Functions and their Applications |
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11 |
Logarithmic Scales |
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12 |
Matrices |
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13 |
Concepts of Matrix algebra |
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14 |
Multiplication of two matrices |
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15 |
Determinant and inverse of 2x2 matrices |
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16 |
Determinant of 3x3 matrix |
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17 |
Solve the systems of equations by Cramer’s Rule |
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18 |
Solve the systems of equations by Inverse Method |
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19 |
Cartesian Coordinate systems |
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20 |
Distance, Mid points and Circles |
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21 |
Concept of Differentiation and Slope of Tangent Line |
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22 |
Solve differentiation by definition |
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23 |
Concepts of Derivatives |
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24 |
Rules for finding derivatives |
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25 |
Power rules of derivatives and its examples |
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26 |
Sum and difference rules of derivatives and its examples |
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27 |
Product and Quotient rules of derivatives and its examples |
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28 |
Derivatives of Trigonometric functions |
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29 |
Derivatives by Chain rules and its examples |
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30 |
Concept of Integration and Area Under the Curves |
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31 |
Integration by Substitution method |
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32 |
Integration by Parts |