Q1
/9
Q2
Q3
/6
/7
Q4
/6
Q5
/8
Q6
/6
Q7
/8
Total
/50
The Australian National University
Midsemester Exam - March 2013
MATH1013 - Mathematics and its Applications I
Book B Algebra
Student No.:
u
Important notes:
You must justify your answers. Do not expect
Continuity
Derivatives
Week 3: Limits, continuity, derivatives of functions
March 4, 2014
Week 3: Limits, continuity, derivatives of functions
Continuity
Derivatives
1
Continuity
Continuous functions
The intermediate value theorem
2
Derivatives
Meaning an
Limits of functions at a point
Limits at innity
Week 2: Limit of Functions
February 26, 2014
Week 2: Limit of Functions
Limits of functions at a point
Limits at innity
1
Limits of functions at a point
2
Limits at innity
Lecture 4
Week 2: Limit of Function
Fundamental Theorem of Calculus
Week 7: Fundamental Theorem of Calculus
March 31, 2014
Week 7: Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
1
Fundamental Theorem of Calculus
FTC and applications
Evaluating integrals
Lecture 14
Week 7: F
Inverse functions
Week 8: Inverse functions
April 23, 2014
Week 8: Inverse functions
Inverse functions
1
Inverse functions
Inverse functions and calculus
Week 8: Inverse functions
Inverse functions
Recall from last class
The substitution rule
If u = g (x)
The natural logarithm
The natural logarithm & exponential
General exponential and logarithmic functions
Week 9: The natural logarithm and exponential
functions
April 24, 2014
Week 9: The natural logarithm and exponential functions
The natural logarithm
Th
General exponential and logarithmic functions
Week 10: Exponential functions, Exponential
growth
May 2, 2014
Week 10: Exponential functions, Exponential growth
General exponential and logarithmic functions
The derivative of e x .
What is the derivative of
Inverse functions
Indeterminate forms
Integration techniques
Week 11: The Inverse Trigonometric Functions,
Hyperbolic Functions, Indeterminate Forms
May 13, 2014
Week 11: The Inverse Trigonometric Functions, Hyperbolic Fun
Inverse functions
Indeterminate
Antiderivatives
Area
Week 6: Optimization, anti-derivatives, denite
integral
March 20, 2014
Week 6: Optimization, anti-derivatives, denite integral
Antiderivatives
Area
1
Antiderivatives
2
Area
Riemann Sums
Denite integral
Lecture 12
Week 6: Optimization,
Linear Approximation
Maxima and Minima
Week 5: Maxima and Minima, Mean Value
Theorem
March 13, 2014
Week 5: Maxima and Minima, Mean Value Theorem
Linear Approximation
Maxima and Minima
1
Linear Approximation
2
Maxima and Minima
The Mean Value Theorem
Deri
Q1
Q2
Q3
Q4
Total
The Australian National University
Midsemester Exam - September 2011
MATH1013 - Mathematics and its Applications I
Part A Calculus
Student No.:
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand written both sid
Q1
Q2
Q3
Q4
Total
The Australian National University
Midsemester Exam - April 2010
MATH1013 - Mathematics and its Applications I
Part A Calculus
Student No.:
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand written both sides p
Q1
/6
Q2
Q3
/5
/6
Q4
/4
Q5
/6
Q6
/7
Q7
/6
Total
/40
The Australian National University
Midsemester Exam - Semester 1, 2016
MATH1013 - Mathematics and its Applications I
Part B Algebra
Student No.:
u
Important notes:
There are two parts to this exam: Part
Q1
Q2
Q3
Q4
Total
The Australian National University
Midsemester Exam - August 2010
MATH1013 - Mathematics and its Applications I
Part A Calculus
Student No.:
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand written both sides
Q1
Q2
Q3
Q4
Total
The Australian National University
Midsemester Exam - April 2009
MATH1013 - Mathematics and its Applications I
Part A Calculus
Student No.:
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand written both sides p
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Total
The Australian National University
Midsemester Exam - September 2010
MATH1013 - Mathematics and its Applications I
Part B Algebra
Student No.
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand wri
Q1
Q2
Q3
Q4
Total
The Australian National University
Midsemester Exam - September 2011
MATH1013 - Mathematics and its Applications I
Part B Algebra
Student No.
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand written on both si
Q1
Q2
Q3
Q4
Total
The Australian National University
Midsemester - April 2010
MATH1013 - Mathematics and its Applications I.
Part B Algebra
Student No.:
Important notes:
You must justify your answers. Be neat.
One A4 sheet hand-written on both sides per
Q1
/6
Q2
Q3
/6
/6
Q4
/6
Q5
/6
Q6
/4
Q7
/6
Total
/40
The Australian National University
Midsemester Exam - August 2014
MATH1013 - Mathematics and its Applications I
Part B Algebra
Student No.:
u
Important notes:
There are two parts to this exam: Part A (C
Techniques of integration
Week 13: Techniques of integration
May 27, 2014
Week 13: Techniques of integration
Techniques of integration
1
Techniques of integration
Trigonometric integrals
The method of partial fractions
Lecture 23
Week 13: Techniques of in
Linear equations
Denition (Linear equation)
A linear equation in variables x1 , . . . , xn is an equation of the form
a1 x1 + a2 x2 + + an xn = b,
where ai and b are scalars (real numbers or complex numbers).
Gri Ware (ANU)
ANU MATH1013 Algebra
Semester 1
Previous Lecture - Standard Matrix
Theorem (THEOREM 10 in Lay)
Let T : Rn Rm be a linear transformation. Then there exists a unique m by n
matrix A such that
T (x) = Ax for all x Rn .
In fact A is the matrix whose jth column is the vector T (ej ), where e
Elementary Matrices
Recall the denition of elementary row operations:
Add a multiple of one row to another row.
Interchange two rows.
Multiply a row by a non-zero constant.
Denition
A matrix obtained from an identity matrix by a single elementary row oper
From Previous Lecture
Theorem (B: Invertibility Characterisations 3 and 4)
For an n n matrix A the following are equivalent:
0
A is invertible.
3
There is an n n matrix C with CA = In . [Statement (j) in Lay Thm. 8]
4
There is an n n matrix D with AD = In
From Previous Lecture
Denition
The column space of a matrix A is the subspace Col A = Span cfw_a1 , . . . , an of
all linear combinations of the columns a1 , . . . , an of A.
Denition
The null space of a matrix A is the subspace Nul (A) of all solutions
16. Properties of Determinants (Lay 3.2)
Cramers Rule, Volume and Linear Transformations (Lay 3.3)
Case Study: http:
/media.pearsoncmg.com/aw/aw_lay_linearalg_3/cs_apps/jacobian.pdf
This will be the last lecture based on content in Lays Linear Algebra tex
Final Exam
The Final Exam will be held:
on Friday, 6 June 2014,
from 14:15 to 17:30
(15 min reading time + 3 hr exam).
The venue is the Sports Hall (Bldg 19).
Permitted materials:
A4 page (1 sheet) with handwritten notes on both sides
Paper-based English-
Q1
/5
Q2
Q3
/5
/6
Q4
/5
Q5
/6
Q6
/9
Q7
/4
Total
/40
The Australian National University
Midsemester Exam - August 2015
MATH1013 - Mathematics and its Applications I
Part B Algebra
Student No.:
u
Important notes:
There are two parts to this exam: Part A (C
MATH 1013 - Mathematics and Its Applications
Tutorial Worksheet 2
1
Algebra
a). Lay(4ed) 1.3 Q16(p32):
Let
and
1
v1 = 0 ,
2
2
v2 = 1 ,
7
h
y = 3 .
5
For what value(s) of h is y in the plane generated by v1 and v2 ?
b). Modified version of Lay(4ed) 1.3 Q
MATH 1013
Practice Quiz 1
Show your work! No calculators allowed.
Our first quiz will be on Monday 79pm at 711 Barry drive. For Linear algebra, questions will be based
on sections 1.1 and 1.2 of the textbook, and Calculus will concentrate on sections 1.31
MATH 1013 - Mathematics and Its Applications
Tutorial Worksheet 1
Please bring this worksheet to the first tutorial. You will also need to to bring a tutorial workbook
which will be used for writing solutions to the Worksheet problems.
1
Algebra
a). Find
The natural logarithm
General exponential and logarithmic functions
Week 9: The natural logarithm and exponential
functions
September 24, 2015
Week 9: The natural logarithm and exponential functions
The natural logarithm
General exponential and logarithmi