- Chapter 1: QUADRATIC EQUATIONS
- Chapter 10: PERIODIC BEHAVIOUR
- Chapter 11: TRIGONOMETRIC EQUATIONS
- Chapter 12: VECTORS AND SCALARS
- Chapter 13: PROBLEMS INVOLVING VECTOR OPERATIONS
- Chapter 14: LIMITS
- Chapter 15: Rules of differentiation
- Chapter 16: Properties of curves
- Chapter 17: Applications of differential calculus
- Chapter 18: Integration
- Chapter 19: Applications of integration
- Chapter 2: RELATIONS AND FUNCTIONS
- Chapter 20: Descriptive statistics
- Chapter 21: Linear modelling
- Chapter 22: Probability
- Chapter 23: Discrete random variables
- Chapter 24: The normal distribution
- Chapter 25: Miscellaneous questions
- Chapter 3: EXPONENTS
- Chapter 4: LOGARITHMS IN BASE 10
- Chapter 5: GRAPHING FUNCTIONS
- Chapter 6: NUMBER SEQUENCES
- Chapter 7: BINOMIAL EXPANSIONS
- Chapter 8: RADIAN MEASURE
- Chapter 9: AREAS OF TRIANGLES
Mathematics for the International Student: Mathematics SL 3rd Edition - Solutions by Chapter
Full solutions for Mathematics for the International Student: Mathematics SL | 3rd Edition
Mathematics for the International Student: Mathematics SL | 3rd Edition - Solutions by ChapterGet Full Solutions
Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.
Upper triangular systems are solved in reverse order Xn to Xl.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.
A = CTC = (L.J]))(L.J]))T for positive definite A.
Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn - l . Cx = convolution c * x. Eigenvectors in F.
Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax - x Tb over growing Krylov subspaces.
Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n - 1)/2 edges between nodes. A tree has only n - 1 edges and no closed loops.
Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.
Incidence matrix of a directed graph.
The m by n edge-node incidence matrix has a row for each edge (node i to node j), with entries -1 and 1 in columns i and j .
Inverse matrix A-I.
Square matrix with A-I A = I and AA-l = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B-1 A-I and (A-I)T. Cofactor formula (A-l)ij = Cji! detA.
Length II x II.
Square root of x T x (Pythagoras in n dimensions).
= Xl (column 1) + ... + xn(column n) = combination of columns.
Nullspace matrix N.
The columns of N are the n - r special solutions to As = O.
The diagonal entry (first nonzero) at the time when a row is used in elimination.
Row space C (AT) = all combinations of rows of A.
Column vectors by convention.
Similar matrices A and B.
Every B = M-I AM has the same eigenvalues as A.
Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).
Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.
Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.