RishanKPLearn
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Semester 1• Course: MAT1001• technical track5 min read

Calculus and Differential Equations

Differential equations, linear algebra, and multivariable calculus for engineers.

Study Progress0 of 4 completed (0%)

Syllabus Units (4)

  1. Unit 1

    Fundamentals of Linear Algebra

    Matrix classifications, row echelon reduction, rank, systems of linear equations, LU decomposition, eigenvalues/eigenvectors, and quadratic forms.

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  2. Unit 2

    Differential Calculus & Multivariable Extrema

    Partial derivatives, Euler’s theorem on homogeneous functions, total differentials, Jacobians, Taylor series expansion, and extrema via Hessian discriminant.

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  3. Unit 3

    Multiple Integrals & Coordinate Systems

    Evaluation of double and triple integrals, change of order of integration, polar/cylindrical coordinates, and area/volume computations in engineering.

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  4. Unit 4

    First-Order Ordinary Differential Equations

    Exact ODEs, integrating factors, first-order linear differential equations, Bernoulli equations, Newton’s law of cooling, and RL/RC circuit transients.

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