Tahun Akademik:
Genap 2021/2022
Kelas-Offr:
D-D
Deskripsi:
Infinite Series: Convergent and Divergent Series, Testing Series for Convergence; the Preliminary Test, Convergence Tests for Series of Positive Terms: Absolute Convergence (The Comparison Test , The Integral Test, The Ratio Test, A Special Comparison Test), Alternating Series; Conditionally Convergent Series, Power Series; Interval of Convergence, Expanding Functions in Power Series, Techniques for Obtaining Power Series Expansions (Multiplying a Series by a Polynomial or by Another Series, Division of Two Series or of a Series by a Polynomial, Binomial Series, Substitution of a Polynomial or a Series for the Variable in Another Series, Combination of Methods, Taylor Series Using the Basic Maclaurin Series), Some Uses of Series. Complex Numbers: Real and Imaginary Parts of a Complex Number, The Complex Plane, Terminology and Notation, Complex Algebra (Simplifying to x+iy form, Complex Conjugate of a Complex Expression, Finding the Absolute Value of z, Complex Equations, Graphs), Complex Infinite Series, Complex Power Series; Disk of Convergence, Elementary Functions of Complex Numbers (Euler’s Formula, Powers and Roots of Complex Numbers), Elementary Functions of Complex Numbers (The Exponential and Trigonometric Functions, Hyperbolic Functions, Logarithms, Complex Roots and Powers, Inverse Trigonometric and Hyperbolic Functions), Some Physical Applications. Vector Analysis: Double and Triple Products, Applications of Vector Multiplication, Differentiation of Vectors, Fields, Directional Derivative; Gradient, Some Other Expressions Involving ∇, Green’s Theorem in the Plane, The Divergence and the Divergence Theorem, The Curl and Stokes’ Theorem. Ordinary Differential Equations: First-Order Equations (Separable Equations, Linear First-Order Equations, Other Methods for First-Order Equations), Second-Order Linear Equations with Constant Coefficients and Zero Right-Hand Side, Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero, Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero, Other Second-Order Equations, The Laplace Transform, Solution of Differential Equations by Laplace Transforms, Convolution, The Dirac Delta Function, A Brief Introduction to Green Functions
Capaian Pembelajaran
Genap 2021/2022
Kelas-Offr:
D-D
Deskripsi:
Infinite Series: Convergent and Divergent Series, Testing Series for Convergence; the Preliminary Test, Convergence Tests for Series of Positive Terms: Absolute Convergence (The Comparison Test , The Integral Test, The Ratio Test, A Special Comparison Test), Alternating Series; Conditionally Convergent Series, Power Series; Interval of Convergence, Expanding Functions in Power Series, Techniques for Obtaining Power Series Expansions (Multiplying a Series by a Polynomial or by Another Series, Division of Two Series or of a Series by a Polynomial, Binomial Series, Substitution of a Polynomial or a Series for the Variable in Another Series, Combination of Methods, Taylor Series Using the Basic Maclaurin Series), Some Uses of Series. Complex Numbers: Real and Imaginary Parts of a Complex Number, The Complex Plane, Terminology and Notation, Complex Algebra (Simplifying to x+iy form, Complex Conjugate of a Complex Expression, Finding the Absolute Value of z, Complex Equations, Graphs), Complex Infinite Series, Complex Power Series; Disk of Convergence, Elementary Functions of Complex Numbers (Euler’s Formula, Powers and Roots of Complex Numbers), Elementary Functions of Complex Numbers (The Exponential and Trigonometric Functions, Hyperbolic Functions, Logarithms, Complex Roots and Powers, Inverse Trigonometric and Hyperbolic Functions), Some Physical Applications. Vector Analysis: Double and Triple Products, Applications of Vector Multiplication, Differentiation of Vectors, Fields, Directional Derivative; Gradient, Some Other Expressions Involving ∇, Green’s Theorem in the Plane, The Divergence and the Divergence Theorem, The Curl and Stokes’ Theorem. Ordinary Differential Equations: First-Order Equations (Separable Equations, Linear First-Order Equations, Other Methods for First-Order Equations), Second-Order Linear Equations with Constant Coefficients and Zero Right-Hand Side, Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero, Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero, Other Second-Order Equations, The Laplace Transform, Solution of Differential Equations by Laplace Transforms, Convolution, The Dirac Delta Function, A Brief Introduction to Green Functions
Capaian Pembelajaran
- Menguasai konsep esensial deret, bilangan kompleks, analisis vektor, persamaan deferensial biasa dan menerapkannya untuk menyelesaikan permasalahan matematika atau fisika yang terkait secara tepat, sistematis, mandiri, bertanggungjawab, dan memanfaatkan perkembangan ipteks
- Mary L. Boas, 2006, Mathematical Methods In The Physical Sciences, 3th edition
- Edwin J Purcell, 2006, Caculus with Differential Equations, 9th edition, Pearson
- Arfken, G. B. dan Weber, H.J., Mathematical Methods for Physicist, 5th ed., Academic Press, 1995
- Teacher: Yoyok Adisetio Laksono