Tahun Akademik:
Genap 2022/2023
Kelas-Offr:
AM-AM
Deskripsi:
Infinite Series, Power Series: 1. The Geometric Series, 2. Definitions and Notation, 3. Applications of Series, 4. Convergent and Divergent Series, 5. Testing Series for Convergence; the Preliminary Test, 6. Convergence Tests for Series of Positive Terms: Absolute Convergence, 7. Alternating Series, 8. Conditionally Convergent Series, 9. Useful Facts About Series, 10. Power Series; Interval of Convergence, 11. Theorems About Power Series, 12. Expanding Functions in Power Series, 13. Techniques for Obtaining Power Series Expansions: A. Multiplying a Series by a Polynomial or by Another Series, B. Division of Two Series or of a Series by a Polynomial, C. Binomial Series, D. Substitution of a Polynomial or a Series for the Variable in Another Series, E. Combination of Methods, F. Taylor Series Using the Basic Maclaurin Series, 14. Accuracy of Series Approximations, 15. Some Uses of Series. Complex Numbers: 1. Introduction, 2. Real and Imaginary Parts of a Complex Number, 3. The Complex Plane, 4. Terminology and Notation, 5. Complex Algebra: A. Simplifying to x+iy form, B. Complex Conjugate of a Complex Expression, C. Finding the Absolute Value of z, D. Complex Equations, E. Graphs, F. Physical Applications, 6. Complex Infinite Series, 7. Complex Power Series; Disk of Convergence, 8. Elementary Functions of Complex Numbers, 9. Euler’s Formula, 10. Powers and Roots of Complex Numbers, 11. The Exponential and Trigonometric Functions, 12. Hyperbolic Functions, 13. Logarithms, 14. Complex Roots and Powers, 15. Inverse Trigonometric and Hyperbolic Functions, 16. Some Applications. Linear Algebra: 1. Introduction, 2. Matrices; Row Reduction, 3. Determinants; Cramer’s Rule, 4. Vectors, 5. Lines and Planes, 6. Matrix Operations, 7. Linear Combinations, Linear Functions, Linear Operators, 8. Linear Dependence and Independence, 9. Special Matrices and Formulas, 10. Linear Vector Spaces, 11. Eigenvalues and Eigenvectors; Diagonalizing Matrices, 12. Applications of Diagonalization. Vector Analysis: 1. Introduction, 2. Applications of Vector Multiplication, 3. Triple Products, 4. Differentiation of Vectors, 5. Fields, 6. Directional Derivative; Gradient, 7. Some Other Expressions Involving ∇, 8. Line Integrals, 9. Green’s Theorem in the Plane, 10. The Divergence and the Divergence Theorem, 11. The Curl and Stokes’ Theorem, 12. Miscellaneous Problems. Ordinary Differential Equations: 1. Introduction, 2. Separable Equations, 3. Linear First-Order Equations, 4. Other Methods for First-Order Equations, 5. Second-Order Linear Equations with Constant Coefficients and Zero Right-Hand Side, , 6. Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero, 7. Other Second-Order Equations, 8. The Laplace Transform, 9. Solution of Differential Equations by Laplace Transforms, 10. Convolution, 11. The Dirac Delta Function, 12. A Brief Introduction to Green Functions.
Capaian Pembelajaran
Genap 2022/2023
Kelas-Offr:
AM-AM
Deskripsi:
Infinite Series, Power Series: 1. The Geometric Series, 2. Definitions and Notation, 3. Applications of Series, 4. Convergent and Divergent Series, 5. Testing Series for Convergence; the Preliminary Test, 6. Convergence Tests for Series of Positive Terms: Absolute Convergence, 7. Alternating Series, 8. Conditionally Convergent Series, 9. Useful Facts About Series, 10. Power Series; Interval of Convergence, 11. Theorems About Power Series, 12. Expanding Functions in Power Series, 13. Techniques for Obtaining Power Series Expansions: A. Multiplying a Series by a Polynomial or by Another Series, B. Division of Two Series or of a Series by a Polynomial, C. Binomial Series, D. Substitution of a Polynomial or a Series for the Variable in Another Series, E. Combination of Methods, F. Taylor Series Using the Basic Maclaurin Series, 14. Accuracy of Series Approximations, 15. Some Uses of Series. Complex Numbers: 1. Introduction, 2. Real and Imaginary Parts of a Complex Number, 3. The Complex Plane, 4. Terminology and Notation, 5. Complex Algebra: A. Simplifying to x+iy form, B. Complex Conjugate of a Complex Expression, C. Finding the Absolute Value of z, D. Complex Equations, E. Graphs, F. Physical Applications, 6. Complex Infinite Series, 7. Complex Power Series; Disk of Convergence, 8. Elementary Functions of Complex Numbers, 9. Euler’s Formula, 10. Powers and Roots of Complex Numbers, 11. The Exponential and Trigonometric Functions, 12. Hyperbolic Functions, 13. Logarithms, 14. Complex Roots and Powers, 15. Inverse Trigonometric and Hyperbolic Functions, 16. Some Applications. Linear Algebra: 1. Introduction, 2. Matrices; Row Reduction, 3. Determinants; Cramer’s Rule, 4. Vectors, 5. Lines and Planes, 6. Matrix Operations, 7. Linear Combinations, Linear Functions, Linear Operators, 8. Linear Dependence and Independence, 9. Special Matrices and Formulas, 10. Linear Vector Spaces, 11. Eigenvalues and Eigenvectors; Diagonalizing Matrices, 12. Applications of Diagonalization. Vector Analysis: 1. Introduction, 2. Applications of Vector Multiplication, 3. Triple Products, 4. Differentiation of Vectors, 5. Fields, 6. Directional Derivative; Gradient, 7. Some Other Expressions Involving ∇, 8. Line Integrals, 9. Green’s Theorem in the Plane, 10. The Divergence and the Divergence Theorem, 11. The Curl and Stokes’ Theorem, 12. Miscellaneous Problems. Ordinary Differential Equations: 1. Introduction, 2. Separable Equations, 3. Linear First-Order Equations, 4. Other Methods for First-Order Equations, 5. Second-Order Linear Equations with Constant Coefficients and Zero Right-Hand Side, , 6. Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero, 7. Other Second-Order Equations, 8. The Laplace Transform, 9. Solution of Differential Equations by Laplace Transforms, 10. Convolution, 11. The Dirac Delta Function, 12. A Brief Introduction to Green Functions.
Capaian Pembelajaran
- Peserta menunjukkan penguasaan terhadap metode matematika Deret Tak Hingga dan Deret Pangkat, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Bilangan Kompleks, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Aljabar Linier, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Analisis Vektor, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Persamaan Deferensial Biasa, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Mary L. Boas, 2006, Mathematical Methods In The Physical Sciences, 3th edition
- Arfken, G. B. dan Weber, H.J., Mathematical Methods for Physicist, 5th ed., Academic Press, 1995
- Teacher: Joko Utomo