Alg I Review: Fill & Download for Free

Calc 1 is commonly known as "differential calculus." You study what is known as the derivative. The derivative is the rate of change of a function or at a certain point on the graph. You'll probably first begin the course doing a quick review of basic algebra 2 and trig concepts that will be important to keep in mind throughout the course: stuff dealing with exponential functions, logarithmic functions, trig graphs, etc. Then you'll get into limits and evaluating them. In this part you may get a brief insight into the formal definition of limits that involves epsilons and deltas (AKA hard shit, well, at first... it made sense after an explanation in class but upon seeing it in a textbook or if you have a shitty professor it can look quite alien). After this you get into the technical/more formal definition of the derivative. Then after this, you'll learn simpler ways and techniques to find derivatives and various theorems and principles related to derivatives, maybe hyperbolic functions and their derivatives. After that, you'll start doing optimization and related rates problems (which is what many people consider to be the hardest part of calc 1). Somewhere around this timeframe, you'll learn about L'Hopital's rule (a way of finding limits involving derivatives), parametric equations, maybe a family of curves (that is what it was called in my textbook) which involves some common functions that pop up in various areas of statistics and stuff. After you cover this stuff, you move from studying the derivative into the integral. You begin studying the integral/antiderivatives by studying areas under curves and using limits and Riemann sums to evaluate these areas under curves. This is sort of the equivalent to the formal definition of the derivative that you will have learned previously. From here, you move into the techniques and common antiderivatives/integrals of basic functions and learn the fundamental theorems of calculus. This is typically where Calc 1 stops.So, in review and in the order in which you'll likely see them... Calc 1 goes something like this.Part I: Introduction to the Fundamentals of Calculus IReview of important Algebra II and Trig concepts that will be a common theme throughout the course.Important graphs from Algebra II (such as exponential curves and logarithmic graphs, inverse stuff, etc)Regarding Trig: Unit circle. Know it and know your identities. They will come in handy.Limitsevaluating/finding limits using various techniquesepsilon delta stuff (You don't learn this in high school calc.... I honestly thought this was the hardest thing I learned in my calc 1 class)Introduction to the derivative (AKA the "rate of change")Finding the derivative at a point (a specific number)Finding the derivative of a function (will involve a variable... this function allows you to find the rate of change at any point along the curve)This will most likely seem obsolete and will leave you frustrated as to why you had to learn this. It involves a lot of algebra and seems unnecessary but it goes to show the importance of limits and gives the formal understanding of what a derivative is.Part II: The Section You Need to Know and Know WellWays of finding derivativesPower ruleProduct ruleQuotient ruleChain rule (this can be confusing the first time you see it)Intermediate Value TheoremMean Value Theorem(optional) Racetrack principle.(optional) Squeeze theoremCommon function derivativesThese will most likely be the functions seen in the Alg 2/Trig review part. There may be some more that weren't in that review, but here are some functions and their derivatives you'll see:SineCosineTangentCosecantSecantCotangente^x or a^x (you'll see why e^x falls into the group of a^x functions)ln(x)x^nArcsineArccosineArctangentHyperbolic SineHyperbolic CosinePart 3 (Using the derivative)OptimizationRelated RatesL'Hopital's RuleParametric Equations(optional) Family of CurvesPart 4: Introduction to the Antiderivative/IntegralYou'll probably start with a D = RT problem and will be told to find total distance by taking the area under the curve (this assumes R and T are constant). Then you'll vary R and will have to find the total distance travelled... this leads to...Using Limits and Riemann Sums to find the area under a curveElementary functions and their antiderivatives (see 2b)Fundamental Theorems of CalculusAnd this is what you will learn in Calc 1. Calc 2 then builds upon these integration techniques and then applies the integral to various kinds of problems. You'll then move into the study of sequences and series and Taylor Polynomials, and maybe a small section on univariate (single variable) differential equations (VERY elementary compared to what is in an actual DE class or partial differential equations class, or a nonlinear dynamics and chaos class). After calc 2 is calc 3 which then leads to a fuller study of linear algebra and differential equations. Have fun.

In my experience (note: this means sample size of 1 + anecdotes from others), the questions are pretty straightforward, by which I mean that anything on the list of prerequisites is fair game. So, this means: you should feel comfortable answering questions covering material from intro stats, intro linear alg, basic programming (particularly related to whatever language you have background in), as well as your usuals like "why do you want to join this program".If it's been awhile since you took the prerequisites mentioned above, it certainly wouldn't hurt to get their terminology back into your head before the interview, so you can speak intelligently and fluently. All in all, I'd say: try not to psych yourself out. At this point, you either have a fairly strong understanding of the prerequisite material, and have good answers regarding what you want out of MSAN and why you want it, or you don't have those things. And reviewing material is just a way of polishing up what's already there if it is there.Good luck.

Calc 1 is commonly known as "differential calculus." You study what is known as the derivative. The derivative is the rate of change of a function or at a certain point on the graph. You'll probably first begin the course doing a quick review of basic algebra 2 and trig concepts that will be important to keep in mind throughout the course: stuff dealing with exponential functions, logarithmic functions, trig graphs, etc. Then you'll get into limits and evaluating them. In this part you may get a brief insight into the formal definition of limits that involves epsilons and deltas (AKA hard shit, well, at first... it made sense after an explanation in class but upon seeing it in a textbook or if you have a shitty professor it can look quite alien). After this you get into the technical/more formal definition of the derivative. Then after this, you'll learn simpler ways and techniques to find derivatives and various theorems and principles related to derivatives, maybe hyperbolic functions and their derivatives. After that, you'll start doing optimization and related rates problems (which is what many people consider to be the hardest part of calc 1). Somewhere around this timeframe, you'll learn about L'Hopital's rule (a way of finding limits involving derivatives), parametric equations, maybe a family of curves (that is what it was called in my textbook) which involves some common functions that pop up in various areas of statistics and stuff. After you cover this stuff, you move from studying the derivative into the integral. You begin studying the integral/antiderivatives by studying areas under curves and using limits and Riemann sums to evaluate these areas under curves. This is sort of the equivalent to the formal definition of the derivative that you will have learned previously. From here, you move into the techniques and common antiderivatives/integrals of basic functions and learn the fundamental theorems of calculus. This is typically where Calc 1 stops.So, in review and in the order in which you'll likely see them... Calc 1 goes something like this.Part I: Introduction to the Fundamentals of Calculus IReview of important Algebra II and Trig concepts that will be a common theme throughout the course.Important graphs from Algebra II (such as exponential curves and logarithmic graphs, inverse stuff, etc)Regarding Trig: Unit circle. Know it and know your identities. They will come in handy.Limitsevaluating/finding limits using various techniquesepsilon delta stuff (You don't learn this in high school calc.... I honestly thought this was the hardest thing I learned in my calc 1 class)Introduction to the derivative (AKA the "rate of change")Finding the derivative at a point (a specific number)Finding the derivative of a function (will involve a variable... this function allows you to find the rate of change at any point along the curve)This will most likely seem obsolete and will leave you frustrated as to why you had to learn this. It involves a lot of algebra and seems unnecessary but it goes to show the importance of limits and gives the formal understanding of what a derivative is.Part II: The Section You Need to Know and Know WellWays of finding derivativesPower ruleProduct ruleQuotient ruleChain rule (this can be confusing the first time you see it)Intermediate Value TheoremMean Value Theorem(optional) Racetrack principle.(optional) Squeeze theoremCommon function derivativesThese will most likely be the functions seen in the Alg 2/Trig review part. There may be some more that weren't in that review, but here are some functions and their derivatives you'll see:SineCosineTangentCosecantSecantCotangente^x or a^x (you'll see why e^x falls into the group of a^x functions)ln(x)x^nArcsineArccosineArctangentHyperbolic SineHyperbolic CosinePart 3 (Using the derivative)OptimizationRelated RatesL'Hopital's RuleParametric Equations(optional) Family of CurvesPart 4: Introduction to the Antiderivative/IntegralYou'll probably start with a D = RT problem and will be told to find total distance by taking the area under the curve (this assumes R and T are constant). Then you'll vary R and will have to find the total distance travelled... this leads to...Using Limits and Riemann Sums to find the area under a curveElementary functions and their antiderivatives (see 2b)Fundamental Theorems of CalculusAnd this is what you will learn in Calc 1. Calc 2 then builds upon these integration techniques and then applies the integral to various kinds of problems. You'll then move into the study of sequences and series and Taylor Polynomials, and maybe a small section on univariate (single variable) differential equations (VERY elementary compared to what is in an actual DE class or partial differential equations class, or a nonlinear dynamics and chaos class). After calc 2 is calc 3 which then leads to a fuller study of linear algebra and differential equations. Have fun.