04-BS-5
Worked solutions to 14 past sittings (2013–2019), 98 questions. Pick a sitting, or start from a topic below.
- December 2019
- December 2018
- May 2018
- December 2017
- May 2017
- December 2016
- May 2016
- December 2015
- May 2015
- December 2014
- May 2014
- December 2013
- May 2013
- Undated paper
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Fixed-Point Iteration (11 sittings): December 2018 Q6 · May 2018 Q6 · December 2017 Q6 · May 2017 Q6 · December 2016 Q6 · December 2015 Q6 · December 2014 Q6 · May 2014 Q6 · December 2013 Q5 · May 2013 Q6 · Undated paper Q6
- Bisection (7 sittings): December 2019 Q6 · December 2018 Q6 · May 2017 Q6 · December 2016 Q6 · December 2015 Q6 · December 2013 Q5 · Undated paper Q6
- Romberg Integration of Tabulated Data (7 sittings): May 2018 Q5 · December 2017 Q5 · December 2016 Q5 · December 2015 Q5 · December 2014 Q5 · December 2013 Q6 · May 2013 Q5
- Lagrange Interpolation (5 sittings): December 2019 Q4 · December 2018 Q4 · December 2017 Q4 · December 2016 Q4 · May 2013 Q4
- Sturm–Liouville Eigenvalue Problem (5 sittings): December 2019 Q1 · December 2018 Q1 · December 2017 Q1 · December 2015 Q1 · May 2014 Q1
- Fourier Series (4 sittings): December 2016 Q2 · December 2015 Q2 · May 2014 Q2 · May 2013 Q2
- Romberg Integration from Tabulated Data (4 sittings): December 2019 Q5 · May 2016 Q5 · May 2015 Q5 · May 2014 Q5
- Area (3 sittings): May 2016 Q3 · December 2014 Q3 · Undated paper Q3
- Cholesky Decomposition (3 sittings): December 2018 Q7 · May 2018 Q7 · May 2016 Q7
- Fourier Transform (3 sittings): May 2016 Q3 · December 2014 Q3 · Undated paper Q3
- LU Decomposition (3 sittings): December 2019 Q7 · December 2014 Q7 · December 2013 Q7
- Newton Divided-Difference Interpolation (3 sittings): May 2018 Q4 · May 2016 Q4 · December 2014 Q4
- Newton's Method (3 sittings): May 2018 Q6 · May 2014 Q6 · December 2013 Q5
- Root-Finding (3 sittings): December 2019 Q6 · December 2018 Q6 · December 2015 Q6
- Solving a Linear System (3 sittings): December 2019 Q7 · May 2014 Q7 · December 2013 Q7
Questions by sitting
December 2019
- Question 1: Sturm–Liouville Eigenvalue Problem
- Question 2: Fourier Series of a Parabolic Arch and Its Derivative
- Question 3: Fourier Transform of a Two-Sided Exponential (Laplace) Pulse
- Question 4: Newton's Divided-Difference and Lagrange Interpolation
- Question 5: Romberg Integration from Tabulated Data
- Question 6: Root-Finding — Newton, Fixed-Point, and Bisection
- Question 7: LU (Doolittle) Decomposition and Solving a Linear System
December 2018
- Question 1: Sturm–Liouville Eigenvalue Problem
- Question 2: Fourier Series of $x^2$ and of Its Derivative
- Question 3: Fourier Transform of a Triangular Pulse
- Question 4: Least-Squares Parabola Proof and Lagrange Interpolation
- Question 5: Romberg Integration and the Area Between Two Curves
- Question 6: Root-Finding — Bisection, Modified Newton, and Fixed-Point Iteration
- Question 7: Cholesky Decomposition and Linear System Solution
May 2018
- Question 1: Power-Series Solution About an Ordinary Point
- Question 2: Fourier Series of a Piecewise-Linear Tent Function
- Question 3: Fourier Transform of a Finite Cosine Window
- Question 4: Least-Squares Parabola Normal Equations & Newton Divided-Difference Interpolation
- Question 5: Romberg Integration of Tabulated Data
- Question 6: Root-Finding by Bisection, Newton's Method, and Fixed-Point Iteration
- Question 7: Cholesky Decomposition and Solution of a Linear System
December 2017
- Question 1: Sturm–Liouville Eigenvalue Problem
- Question 2: Fourier Series of a Piecewise-Quadratic Function
- Question 3: Fourier Transform of a Two-Sided Exponential
- Question 4: Lagrange Interpolation and Forward-Difference Derivatives
- Question 5: Romberg Integration of Tabulated Data
- Question 6: Fixed-Point Iteration, Bisection/Newton, and Extrema of a Quartic
- Question 7: Crout LU Decomposition and Linear System Solution
May 2017
- Question 1: Power-Series Solution about an Ordinary Point
- Question 2: Fourier Series of a Square Wave and the Leibniz Series
- Question 3: Fourier Transform of a Raised-Cosine Pulse
- Question 4: Newton’s Divided-Difference Interpolation
- Question 5: Romberg Integration from a Table
- Question 6: Bisection, Newton–Raphson and Fixed-Point Iteration
- Question 7: Cayley–Hamilton, Matrix Inversion and a Linear System
December 2016
- Question 1: Power Series Solution of a Linear ODE
- Question 2: Fourier Series and Term-by-Term Differentiation
- Question 3: Fourier Transform of a Triangular Pulse
- Question 4: Least-Squares Parabola Proof and Lagrange Interpolation
- Question 5: Romberg Integration of Tabulated Data
- Question 6: Bisection, a Second-Order Iterative Method, and Fixed-Point Iteration
- Question 7: Cholesky-Type Factorization of a Symmetric Positive-Definite Matrix
May 2016
- Question 1: Power-Series Solution of $y''-4xy=0$
- Question 2: Fourier Series of a Saturating Triangular Wave
- Question 3: Windowed-Cosine Pulse — Area and Fourier Transform
- Question 4: Least-Squares Normal Equations and Newton Divided-Difference Interpolation
- Question 5: Romberg Integration from Tabulated Data
- Question 6: Modified Newton’s Method for a Root and a Minimum
- Question 7: Cholesky ($LL^{T}$) Decomposition and Linear-System Solve
December 2015
- Question 1: Sturm–Liouville Eigenvalue Problem
- Question 2: Fourier Series and a Classical Identity
- Question 3: Fourier Transform of a Two-Sided Exponential Pulse
- Question 4: Polynomial Interpolation — Newton Divided Differences and Lagrange
- Question 5: Romberg Integration of Tabulated Data
- Question 6: Root-Finding — Newton, Fixed-Point Iteration, and Bisection
- Question 7: Doolittle LU Decomposition and Linear System Solve
May 2015
- Question 1: Power-series solution of a second-order ODE
- Question 2: Fourier series of $F(x)=x^2$ and the Basel-sum identity
- Question 3: Fourier transform of a triangular pulse
- Question 4: Least-squares parabola (proof) and a linear least-squares fit
- Question 5: Romberg integration from tabulated data
- Question 6: Root finding by bisection then Halley's iteration
- Question 7: Cholesky factorization of a symmetric positive-definite matrix
December 2014
- Question 1: Power-Series Solution of a Variable-Coefficient ODE
- Question 2: Fourier Series of an Odd Function and a Series Identity
- Question 3: Laplace-Kernel Function — Area, Fourier Transform, and the $a\to0$ Limit
- Question 4: Newton Divided-Difference Interpolation and Numerical Differentiation
- Question 5: Romberg Integration of Tabulated Data
- Question 6: Newton’s Method and Fixed-Point Iteration
- Question 7: LU (Crout) Decomposition and Solution of a Linear System
May 2014
- Question 1: Sturm–Liouville Eigenvalue Problem
- Question 2: Fourier Series and a Classical Series Identity
- Question 3: Fourier Transform of a Trapezoidal Pulse
- Question 4: Least-Squares Curve Fitting and an Interpolating Polynomial
- Question 5: Romberg Integration from Tabulated Data
- Question 6: Root-Finding by Bisection, Newton's Method, and Fixed-Point Iteration
- Question 7: Cholesky Factorization and Solving a Linear System
December 2013
- Question 1: Power-Series Solution of a Legendre-Type ODE
- Question 2: Fourier Series of a Piecewise Function
- Question 3: Two-Sided Exponential and Its Fourier Transform
- Question 4: Newton's Divided Differences and Finite-Difference Derivatives
- Question 5: Newton's Method, Bisection, and Fixed-Point Iteration
- Question 6: Romberg Integration of Tabulated Data
- Question 7: LU Decomposition and Solving a Linear System
May 2013
- Question 1: Power-Series Solution of a Second-Order ODE
- Question 2: Fourier Series and a Classical Series Identity
- Question 3: A Cosine Pulse and Its Fourier Transform
- Question 4: Least-Squares Parabola and Lagrange Interpolation
- Question 5: Romberg Integration of Tabulated Data
- Question 6: Root-Finding by Halley-Form Iteration and Fixed-Point Iteration
- Question 7: Cayley–Hamilton Theorem, Matrix Inverse, and a Linear System
Undated paper
- Question 1: Power-Series Solution about an Ordinary Point
- Question 2: Fourier Series of a Piecewise-Linear Wave and a Series Identity
- Question 3: Area, Fourier Transform and Limiting Behaviour of a Raised-Cosine Pulse
- Question 4: Newton's Divided-Difference Interpolating Polynomial
- Question 5: Romberg Integration of a Tabulated Experimental Curve
- Question 6: Bisection, Newton–Raphson and Fixed-Point Iteration
- Question 7: Matrix Inverse by the Cayley–Hamilton Theorem