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Class Notes for Mathematics at Simon Fraser University

MATH 154 Lecture Notes - Lecture 38: Inverse Trigonometric Functions, Visual Angle, Implicit Function
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MATH 154: Week 13 Lecture 3 -to derive inverse trigonometric functions, use implicit differentiation -y = arcsin(x), and sin(y) = x -so sin = = 1 -cos = 1 1 1 - = = 2 cos() 1 -we cant leave cos(y) as it is, since we want t...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture 37: Trigonometry Derivatives
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MATH 154: Week 13 Lecture 2 -with plot-space diagrams, we need to include a graph a table -we should be able to draw parabolas (for exams) - + = 1 2 2 - 2 + 2 = 1 2 2 - 3 + 3 = 1 -sin + sin + sin() -sin + = sin cos + sin ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 20: Crop Yield, Maxima And Minima, Logistic Function
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MATH 154: Week 7 Lecture 3 -for the logistic growth equation = ( ), r is the intrinsic growth rate -K is the carrying capacity, or the maximum population density ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 36: Inverse Function
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MATH 154: Week 13 Lecture 1 -the functions sin and cos are periodic with period 2 because: -sin 2 + = -cos 2 + = - = sin( + 2) for any value of k that is an integer -this goes for cos as well -trig functions are not invert...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 35: Radian, Unit Circle, Logistic Function
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MATH 154: Week 12 Lecture 3 -with the logistic growth function = ()(1 ), it is first order non-linear -in trigonometry, the functions sin and cos are defined by the fact that (cos, sin ) are the coordinates of a point on ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 34: Slope Field
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MATH 154: Week 12 Lecture 2 - tells us about the slope of a function -when slope is 0, the tangent line is horizontal -the slope field shows the tangent lines of the original curve, so it gives information about the shape ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture 33: Euler's Method & Differential Equation Summary
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MATH 154: Week 12 Lecture 1 -the final is going to be about 20 material from the first midterm, 20 material from nd nd the 2 midterm, and 60 material from after the 2 midterm -with the equation = ,) is proportional to the ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture 21: Optimization & Closed Interval Method
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MATH 154: Week 8 Lecture 1 -with many optimization problems, there are 2+ variables and additional constraints -with these problems, we must use the constraints to reduce the function to 1 variable, then solve -eg. find th...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture 32: solving differential equations
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MATH 154: Week 11 Lecture 2 - () = 5 5 -( )= 5 -( )= -the rate of change of this function is proportional to itself -if we have = with y(0) = y 0 then = 0 5 -eg. if = 5 with y(0) = 100, then = 100 -solving differential equ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 31: Exponential Decay, Doubling Time
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MATH 154: Week 11 Lecture 1 x -we know that for the function y = e , it satisfies = -a differential equation is an equation where both sides are functions (funct...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 18: Maxima And Minima
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MATH 154: Week 7 Lecture 1 -a function f(x) has a local minimum at a point if the value of f at that point is smaller than the value of f at all nearby points -a function f(x) has a local maximum at a point if the value of...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 17: Differentiable Function
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MATH 154: Week 6 Lecture 2 -on which intervals is = 92positive? ( 1) (+1)(1) -first factor it; (3)(3+) (3)(3+) -f may change value at any point where it is 0 or undefined sign of -3 -1 0 1 3 x - - - + + + x-1 - - - - + + x...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture Notes - Lecture 5: Asymptote, Classification Of Discontinuities
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MATH 154: Week 2 Lecture 3 -a limit is a value you hope to get (may not get that value); very important concept for calculus -right-hand & left-hand limits may be different -a limit at a exists if & only if both left-ha...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture 3: Domains, Zeroes, & Even/Odd Functions
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MATH 154: Lecture 2 1 - or is not a polynomial, because it does not have an integer exponent -power functions, polynomials, and rational functions all have many uses in the life sciences domain: for a function, the set of ...

Mathematics
MATH 154
Yusuf Tuncer
MATH 154 Lecture 29: Differentiating Exponential Functions & Doubling
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MATH 154: Week 10 Lecture 2 x -e and ln(x) are the inverse of each other ln() - ln )) = = - ln )= ln( ) ln() -for ...

Mathematics
MATH 154
Yusuf Tuncer
Statistics - Reference Guides

This Guide provides an easy to follow summary of all basic principles that are the foundation to Statistics and Probabilities. Using a combination of charts and sample equations, the key concepts are developed and the esse...

Econometrics
ETC2430
All Professors
Calculus Derivatives - Reference Guides

This advanced Calculus Guide provides assistance to the user through its articulation of key Derivatives principles. Helpful tips to solve exponential and logarithmic functions are featured.

BAD - Business Administration
BAD 200
All Professors
Permachart - Marketing Reference Guide: Becquerel, Hyperbolic Function, International Standard Book Number

l e a r n • r e f e r e n c e • r e v i e w permacharts TM CCalculus Integrals II INTEGRALS INVOLVING a+bu & p+qu ...

BAD - Business Administration
BAD 200
All Professors
College Mathematics - Reference Guides

This comprehensive Guide provides concrete reference materials in three math fundamentals – Algebra, Calculus, and Trigonometry. Helpful sample equations and rules are the backbone to this Guide

BAD - Business Administration
BAD 200
All Professors
Permachart - Marketing Reference Guide: Inflection Point, Inflection, Farad

l e a r n • r e f e r e n c e • r e v i e w permacharts TM Differential Calculus Differential Calculus ...

BAD - Business Administration
BAD 200
All Professors
Permachart - Marketing Reference Guide: Iterated Integral, Centroid, Multiple Integral

permacht asrTM integral Calculus theorems types of iNtegrals averaGe value Theorem ...

BAD - Business Administration
BAD 200
All Professors
Laplace Transforms - Reference Guides

This useful Math Guide is a specific reference for techniques to convert ordinary differential equations to algebraic equations. Helpful charts and summaries are used to convey information such as exponential, square root,...

BAD - Business Administration
BAD 200
All Professors
Permachart - Marketing Reference Guide: Charge Pump, Diode, Electrolytic Capacitor

l e a r n • r e f e r e n c e • r e v i e w permacharts TM CConductors & Semiconductors BASICS TERMS Conductor Valence and conduction bands for electr...

Electrical Engineering
4400:307
All Professors
Permachart - Marketing Reference Guide: Steradian, Luminous Intensity, Si Base Unit

l e a r n • r e f e r e n c e • r e v i e w permacharts TM Metric System ...

Basic Engineering
BE 1101
All Professors
Intermediate Algebra - Reference Guides

This more advanced Guide builds upon the reference material set out in the Introductory Algebra Guide. Linear equations, polynomial equations and complex numbers are readily explained; clear and easy to follow emphasis is ...

MATH
MATH 504
All Professors
Introductory Algebra - Reference Guides

This Guide provides a concise and very readable summary of all key Algebraic principles. Special attention is directed to terminology, laws, and operations, with practical examples developed as illustration of these princi...

MATH
MATH 504
All Professors
Permachart - Marketing Reference Guide: Circumscribed Circle, Trapezoidal Rule, Quadrilateral

permacharts TM Geometry Geometry QUADRILATERALS CIRCLES & CONICS...

MATH
MATH 501
All Professors
Permachart - Marketing Reference Guide: Cubic Yard, Nautical Mile, Fluid Ounce

l e a r n • r e f e r e n c e • r e v i e w permacharts TM Weights & Measures THE U.S./IMPERIAL SYSTEM OF MEASUREMENTS ...

Physics
PHYS 24300
All Professors
Vectors & Matrices - Reference Guides

Vectors are an important area of study that develops naturally from a basic understanding of physics and is subsets – statics, dynamics, and mechanics. This practical Guide provides assistance in an often complex disciplin...

Physics
PHYS 24300
All Professors
Permachart - Marketing Reference Guide: Luminous Flux, Magnetic Flux, Magnetic Flux Quantum

permacharts TM F u n d a m e n t a lP h y s ic a lC o n s t a n t s General Constants Quantity...

Physics
PHYS 24300
All Professors

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