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Aryabhatta Knowledge University, Bihar, Civil Engineering Semester 1, Mathematics –I ( Calculus, Multivariable Calculus and Linear Algebra ) Syllabus
Mathematics –I ( Calculus, Multivariable Calculus and Linear Algebra ) Lecture notes | Videos | Free pdf Download | Previous years solved question papers | MCQs | Question Banks| Syllabus
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Unit - 1A CALCULUS
Unit 1Calculus
1.1 Evolutes and Involutes
1.2 Evaluation of Definite and Improper Integrals
1.3 Beta and Gamma Functions and Their Properties
1.4 Applications of Definite Integrals to Evaluate Surface Areas and Volumes of Revolutions
1.5 Rolle’s Theorem
1.6 Mean Value Theorems
1.7 Taylor’s and Maclaurin Theorems with Remainders
1.8 Indeterminate Forms and Lhospitals Rule
1.9 Maxima and Minima
Unit - 1B CALCULUS
Unit 2Sequence and series
2.1 Convergence of Sequence and Series
2.2 Tests for Convergence Power Series
2.3 Taylors Series
2.5 Trigonometric and Logarithmic Functions
2.6 Fourier Series Half Range Sine and Cosine Series
2.7 Parseval’s Theorem
Unit - 1C SERIES
Unit 3Multivariable calculus Differentiation
3.1 Limit Continuity and Partial Derivatives
3.2 Directional Derivatives
3.3 Total Derivative
3.4 Tangent Plane and Normal Line
3.5 Maxima Minima and Saddle Points
3.6 Method of Lagrange Multipliers
3.7 Gradient Curl and Divergence
Unit - 2A MATRICES
Unit 4Multivariable calculus Integration
4.1 Multiple Integration Double and Triple Integrals Cartesian and Polar
4.2 Change of Order of Integration in Double Integrals
4.3 Change of Variables Cartesian to Polar
4.5 Center of Mass and Gravity Constant and Variable Densities
4.6 Theorems of Green Gauss and Stokes
4.7 Orthogonal Curvilinear Coordinates
4.8 Simple Applications Involving Cubes Sphere and Rectangular Parallelepipeds
Unit - 2B MATRICES
Unit 5First order ordinary differential equations
5.1 Exact Linear and Bernoulli’s Equations
5.2 Euler’s Equations
5.3 Equations Not of First Degree Equations Solvable For P Equations Solvable For Y Equations Solvable for X And Clairaut’s Type
Unit - 2C VECTOR SPACES
Unit 6Ordinary differential equations of higher order
6.1 Second Order Linear Differential Equations with Variable Coefficients
6.2 Method of Variation of Parameters
6.3 CauchyEuler Equation
6.4 Power Series Solutions
6.5 Legendre Polynomials
6.6 Bessel Functions of The First Kind and Their Properties
Unit - 2D VECTOR SPACES
Unit 7Partial differential equations First Order
7.1 First Order Partial Differential Equations
7.2 Solutions of First Order Linear and NonLinear PDES
Unit 7
Partial differential equations First Order
7.1 First Order Partial Differential Equations
7.2 Solutions of First Order Linear and NonLinear PDES
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