<p>I'm doing BC as a junior, and since there are like 6others, it's a pretty big deal. We had to skip 7th grade "Pre-Algebra" and take Algebra I as 7th graders to skip ahead.</p>
<p>Token Adult -- Just saw your query about books! </p>
<p>DS1 (a junior) is taking MV this semester -- they are using Swokowski's Calculus w/Analytic Geometry, 3rd ed., Prindle Weber & Schmidt, pub., 1984. (old school book, "old school" teacher.) Works out great. DS1 is taking DiffEq next semester, and says they will be going to another book then.</p>
<p>His teacher told us that every year, he gets emails from profs asking about placement for incoming freshmen who've already had MV and questioning the students' insistence that they be placed out. The teacher tells them the books he uses, sends a sample exam, and the profs are satisfied. My spouse says what DS1 is doing is harder than the Calc III course he took at Penn (Math 242, if I remember correctly)</p>
<p>Topics for MV and DiffEq courses include:
Vectors and Analytic Geometry
Vectors in a Plane
Rectangular Coordinate System in Three Dimensions
Vectors in Space
The Dot and Cross Products
Parametric Equations in Space
Planes
Cylinders and Surfaces of Revolution
Quadric Surfaces
Vector-Valued Functions
Definitions
Limits, Derivatives, and Integrals
Motion
Curvature
Tangential and Normal Components of Acceleration
Kepler's Laws
Partial Differentiation
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Increments and Differentials
The Chain Rule
Directional Derivatives and Gradients
Tangent Planes and Normal Lines to Surfaces
Extrema of Functions of Several Variables
LaGrange Multipliers
Multiple Integrals
Double Integrals
Evaluation of Double Integrals
Areas and Volumes
Moments and Center of Mass
Double Integrals in Polar Coordinates
Triple Integrals
Applications of Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Vector Analysis
Vector Fields
Line Integrals
Independence of Path
Green's Theorem
Surface Integrals
The Divergence Theorem
Stokes' Theorem
Transformation of Coordinates
Change of Variables in Multiple Integrals
More Differential Equations
Review of First Order Differential Equations
Higher Order Linear Differential Equations
Series Solutions of Differential Equations
Applications </p>
<p>This is the syllabus for Complex Analysis, which he'll take next fall:
Complex Number System
Definition of the Complex Number System
Fundamental Operations with Complex Numbers
Algebraic Properties of Complex Numbers
Geometric Interpretation of Complex Numbers
Further Properties of Moduli
Polar Form
Exponential Form
Powers and Roots
Regions in the Complex Plane
Spherical Representation of Complex Numbers
Dot and Cross Products
Analytic Functions
Functions of a Complex Variable
Mappings
Limits
Theorems on Limits
Continuity
Derivatives
Differentiation Formulas
Cauchy-Riemann Equations
Sufficient Conditions for Analycity
Polar Coordinates
Analytic Functions
Harmonic Functions
Elementary Functions
The Exponential Function
Other Properties of exp z
Trigonometric Functions
Hyperbolic Functions
The Logarithmic Functions and Its Branches
Further Properties of Logarithms
Complex Exponents
Inverse Trigonometric and Hyperbolic Functions
Complex Integration
Definite Integrals of w(t)
Contours
Line Integrals and Examples
Cauchy-Goursat Theorem
Preliminary Lemma
Proof of the Cauchy-Goursat Theorem
Simply and Multiply Connected Domains
Antiderivatives and Independence of Path
Cauchy Integral Formula
Derivatives of Analytic Functions
Morera's Theorem
Maximum Moduli of Functions
Liouville's Theorem and the Fundamental Theorem of Algebra
Infinite Series
Convergence of Sequences and Series
Taylor Series
Observations and Examples
Laurent Series
Further Properties of Series
Uniform Convergence
Integration and Differentiation of Power Series
Uniqueness of Series
Representations
Multiplication and Division of Series
Examples
Zeros of Analytic Functions
Residues and Poles
Residues
Calculation of Residues
The Residue Theorem
Principal Part of a Function
Residues at Poles
Quotients of Analytic Functions
Evaluation of Improper Real Integrals
Improper Integrals Involving Sines and Cosines
Definite Integrals Involving Sines and Cosines
Integration through a Branch Cut
Mappings By Elementary Functions
Linear Functions
The Function 1/z
Linear Fractional Transformations
Special Linear Fractional Transformations
The Function z2
The Function square root of z
Related Functions
The Transformation of w = exp z
The Transformation of w = sin z
Successive Transformations
Table of Transformations of Regions
Conformal Mappings
Basic Properties
Further Properties and Examples
Harmonic Conjugates
Transformations of Harmonic Functions
Transformations of Boundary Condition</p>
<p>CountingDown, please remind me, is the complex analysis a high school course, or is that taken at a local college?</p>
<p>TokenAdult,
It's at the high school. :) I can PM you more...I meant to do this a while ago and never had the chance.</p>
<p>I thought real analysis was necessary for complex analysis. Would one of you mind explaining the difference? I'm trying to figure out what math class to take next semester and I'm not entirely sure what everything is.</p>
<p>Usually, a complex analysis course would follow a real analysis course, but courses can be harder or easier with either of those labels.</p>
<p>Only Junior in my BC calc class (20+ in all)</p>
<p>Theres a soph in AB in my school</p>
<p>7th grade: geometry
8th grade: alg2/precalc/trig
9th grade: calc bc
10th grade: slackslack
11th: grade: slack too much -> drop outta high school</p>
<p>/end brag</p>
<p>I'm not in Calc, but I wish I was. I moved in from a different school system where they only had Algebra in Middle School. So I can't really move up. It's kind of strange because the people who don't really like math are in a higher class than the ones who like it. </p>
<p>There's only like 1 person as a junior taking Calc BC and like 40 taking Calc AB.</p>
<p>Do most other schools require you to take Calc. AB before BC? I'm a sophomore taking Calc. BC, but I haven't taken Calc. AB. Our calculus class is longer than the average class, and, according to the instructor, semester one will cover the AB portion and semester two will cover the BC portion. Is this common? And also, what do most of you take after Calc. BC? I have a choice between Multivariable Calc., Differential Equations, and Linear Algebra for junior and senior year.</p>
<p>BC in 10th grade, took Honors Calc III-IV at Columbia in 11th. Taking AP Stats my senior year just because I need a "math course" >.<</p>
<p>Potential:</p>
<p>Multivariate Calculus.</p>
<p>Thanks, BoelterHall.</p>
<p>Do so in the order: Multivariate Calculus, DE, Linear Algebra.</p>
<p>Multivariate Calculus (1st half) is quite simple, up to Lagrange Multipliers. Starting with double and triple integrals, it gets tricky. Good luck with your studies.</p>
<p>From what I understand from others with far more expertise than I, Linear Alg does not require MV and DiffEq. DS1's school will let you take it after BC Calc. That said, it is probably better to go straight from Calc BC to MV and DiffEq just to keep the material fresh, if you want to take all three courses while in HS.</p>
<p>Some of the current courses do as my son's course does, and set the sequence as Calc C topics (which includes very elementary differential equations problems), followed by a LOT of linear algebra, before going to multivariable calculus and rather more differential equations in the multivariable calculus. That's supposed to allow using linear algebra as a tool in the later topics.</p>
<p>yea. taking calc ab this year. it's not that big of a deal at my school though.</p>
<p>There are maybe only 30 kids (juniors and seniors) taking cal AB in my public school (~3000) kids. I think cal BC is only 10 seniors this year, and some years there's not even a cal bc class.</p>
<p>what percentage of multiple choice questions and total points do you need on the ap to get a 4 and 5?</p>
<p>
</p>
<p>Lucky You!!!</p>
<p>I am doing Calc BC (1st Semester CalcAB 2nd Semester Calc BC) in my Junior
Year but this is unfortunately unusual at my school.</p>
<p>I am planning on Self studying Multivariable calculus and Linear Algebra
using EPGY next. ...possible paths to follow are nicely
illustrated at: <a href="http://epgy.stanford.edu/overview/faq.html#uniplace">http://epgy.stanford.edu/overview/faq.html#uniplace</a> </p>