Mathematics 103 - Notes for Lecture 31
1
Complex Numbers
Outcomes In todays lecture we will learn how to:
Perform basic complex arithmetic.
Plot complex numbers in the Complex Plane.
Contents
Complex numbers in terms of real and imaginary parts.
Addit

Mathematics 103 - Notes for Lecture 33
1
Complex Numbers
Outcomes In todays lecture we will learn how to:
Define regions in the complex plane from a variety of different types of inequalities.
Carry out multiplication and division in polar form.
Use De

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Mathematics 103 - Notes for Lecture 23
1
Systems of Linear Equations
Outcomes In todays lecture we will learn how to:
Recognize the three basic scenarios that can arise when solving systems of linear
equations.
Recognize a row echelon form.
Solve for a

Mathematics 103 - Notes for Lecture 34
1
Complex Numbers
Outcomes In todays lecture we will learn how to:
Determine all n-th roots of a complex number.
Find the roots of simple, low order, polynomial equations.
Contents
The roots of a complex number.

Mathematics 103 - Notes for Lecture 22
1
Introduction to Matrices
Outcomes In todays lecture we will learn how to:
Recognize a matrix as a 2 dimensional array.
Add, multiply and transpose matrices.
Recognize square and symmetric matrices.
Identify inv

Mathematics 103 - Notes for Lecture 32
1
Complex Numbers
Outcomes In todays lecture we will learn how to:
Convert between the polar and the Cartesian form of a complex number.
Define regions in the complex plane from a variety of different types of ineq

Mathematics 103 - Notes for Lecture 29
1
Eigenvalues and Eigenvectors
Outcomes In todays lecture we will learn how to:
Calculate eigenvalues for small scale matrices.
Contents
Scaling, reflections and rotations of vectors in the plane.
Eigenvalues and

Mathematics 103 - Notes for Lecture 27
1
Determinants
Outcomes In todays lecture we will learn how to:
Evaluate determinants of larger matrices by first applying appropriate elementary
row or column operations.
Identify the relationship between the dete

Mathematics 103 - Notes for Lecture 30
1
Finding Eigenvectors
Outcomes In todays lecture we will learn how to:
Determine eigenvectors for small scale matrices.
Contents
Eigenvectors as solutions of homogeneous systems of equations.
A variety of example

Mathematics 103 - Notes for Lecture 24
1
Gaussian Elimination
Outcomes In todays lecture we will learn how to:
Recognize the type of solution of a linear system by identifying the ranks of the
coefficient and augmented matrices.
Describe infinitely many

Mathematics 103 - Notes for Lecture 28
1
Linear Dependence & Independence
Outcomes In todays lecture we will learn how to:
Determine whether a given vector is a linear combination of others or not.
Establish the linear dependence or independence of a gi

Mathematics 103 - Notes for Lecture 21
1
Lines in 3 Space
Outcomes In todays lecture we will learn how to:
Identify a line from its equation and vice versa.
Determine distances between points and lines.
Contents
Vector and parametric equations of a lin

In summary, testing for l.i. or l.d.
(i) If there only two vectors check to see if
theyre parallel, i.e. v1 = sv2. If they are
parallel then theyre l.d., else theyre l.i.
If there are more than two vectors go to
(ii).
(ii) Check to see if the number of ve

Mathematics 103 - Notes for Lecture 26
1
Inverses and Determinants
Outcomes In todays lecture we will learn how to:
Identify in which circumstances it is advantageous to solve Ax = b as x = A1 b.
Calculate determinants of square matrices of any size.
Co

Mathematics 103 - Notes for Lecture 25
1
More on Linear Systems
Outcomes In todays lecture we will learn how to:
Recognize the special nature of homogeneous systems and understand the associated
terminology.
Determine the inverse of a matrix by the Gaus

Mathematics 103 - Notes for Lecture 14
1
Areas
Outcomes In todays lecture we will learn how to:
Calculate areas in the plane bounded by simple curves.
Understand the importance of odd and even functions when integrating over a symmetric interval of inte

Mathematics 103 - Notes for Lecture 18
1
Vector Geometry
Outcomes In todays lecture we will learn how to:
Work with vectors in a geometric as well as in an algebraic setting.
Understand the distinction between notation for a point and vector.
Recognize

Mathematics 103 - Notes for Lecture 15
1
The Natural Logarithm
Outcomes In todays lecture we will learn how to:
Understand the meaning of the natural logarithm.
Differentiate expressions involving ln.
Evaluate integrals of the form
R f 0 (x)
f (x)
dx.

Mathematics 103 - Notes for Lecture 20
The Cross Product and Applications
Outcomes In todays lecture we will learn how to:
Calculate the cross product.
Determine a cross product geometrically.
Determine areas of parallelograms and volumes of parallelep

Mathematics 103 - Notes for Lecture 19
1
Vector Geometry
Outcomes In todays lecture we will learn how to:
Work in standard unit basis vector notation.
Understand and use of the two versions of the dot product.
Determine scalar and vector projections.

Mathematics 103 - Notes for Lecture 16
1
Exponential and other Logarithm Functions
Outcomes In todays lecture we will learn how to:
Differentiate and integrate expressions involving exponentials.
Solve elementary equations involving logarithms and expon

Mathematics 103 - Notes for Lecture 13
1
Definite Integrals
Outcomes In todays lecture we will learn how to:
Understand the meaning of a definite integral.
Evaluate elementary definite integrals.
Differentiate functions of the form F (x) =
Z g(x)
f (t)

Mathematics 103 - Notes for Lecture 4
1
Trigonometric Functions
Outcomes In todays lecture we will learn how to:
Convert measurements of angles between degrees and radians.
Resolve right angled triangles through the use of trigonometric ratios.
Underst

Mathematics 103 - Notes for Lecture 2
1
Limits and Asymptotes
Outcomes In todays lecture we will learn how to:
Determine elementary limits of functions and use these to help sketch their graphs.
Recognize discontinuities of functions and their type.
Con

Mathematics 103 - Notes for Lecture 6
1
Trigonometric Equations and Periodic Functions
Outcomes In todays lecture we will learn how to:
Correctly apply the sine or cosine rules to resolve general triangles.
Recognize periodic functions and determine the

Mathematics 103 - Notes for Lecture 11
1
Applications of Differentiation
Outcomes In todays lecture we will learn how to:
Solve elementary optimization problems.
Understand how first and second derivative values lead to certain graphical features.
Conte

Mathematics 103 - Notes for Lecture 12
1
Indefinite Integrals
Outcomes In todays lecture we will learn how to:
Solve elementary integration problems.
Evaluate basic integrals requiring a substitution quickly and accurately.
Contents
The idea of an inde

Mathematics 103 - Notes for Lecture 10
1
Further Differentiation
Outcomes In todays lecture we will learn how to:
Recognize when implicit differentiation is required and knowledge of how to apply
it.
Find the linear approximation of a function.
Underst

Mathematics 103 - Notes for Lecture 5
1
Trigonometric Functions
Outcomes In todays lecture we will learn how to:
Sketch the graphs of the basic trigonometric functions and identify their basic features.
Classify functions as odd, even or neither.
Under