add section landing pages

quarto/ODEs.qmd

@@ -0,0 +1,3 @@
+# ODEs
+
+Ordinary differential equations are equations involving derivatives of an unknown function. Such equations may be more naturally derived from physical models. In many cases, the function can be solved for algebraically. In others, the function can be numerically estimated.

quarto/_quarto.yml

@@ -24,7 +24,7 @@ book:
   page-footer: "Copyright 2022, John Verzani"
   chapters:
     - index.qmd
-    - part: "Precalculus Concepts"
+    - part: precalc.qmd
       chapters:
         - precalc/calculator.qmd
         - precalc/variables.qmd
@@ -44,14 +44,14 @@ book:
         - precalc/trig_functions.qmd
         - precalc/julia_overview.qmd
 
-    - part: "Limits"
+    - part: limits.qmd
       chapters:
         - limits/limits.qmd
         - limits/limits_extensions.qmd
         - limits/continuity.qmd
         - limits/intermediate_value_theorem.qmd
 
-    - part: "Derivatives"
+    - part: derivatives.qmd
       chapters:
         - derivatives/derivatives.qmd
         - derivatives/numeric_derivatives.qmd
@@ -68,7 +68,7 @@ book:
         - derivatives/related_rates.qmd
         - derivatives/taylor_series_polynomials.qmd
 
-    - part: "Integrals"
+    - part: integrals.qmd
       chapters:
         - integrals/area.qmd
         - integrals/ftc.qmd
@@ -83,14 +83,14 @@ book:
         - integrals/arc_length.qmd
         - integrals/surface_area.qmd
 
-    - part: "ODEs"
+    - part: ODEs.qmd
       chapters:
         - ODEs/odes.qmd
         - ODEs/euler.qmd
         - ODEs/solve.qmd
         - ODEs/differential_equations.qmd
 
-    - part: "Differential vector calculus"
+    - part: differentiable_vector_calculus.qmd
       chapters:
         - differentiable_vector_calculus/polar_coordinates.qmd
         - differentiable_vector_calculus/vectors.qmd
@@ -100,7 +100,7 @@ book:
         - differentiable_vector_calculus/vector_fields.qmd
         - differentiable_vector_calculus/plots_plotting.qmd
 
-    - part: "Integral vector calculus"
+    - part: integral_vector_calculus.qmd
       chapters:
         - integral_vector_calculus/double_triple_integrals.qmd
         - integral_vector_calculus/line_integrals.qmd

quarto/derivatives.qmd

@@ -0,0 +1,3 @@
+# Derivatives
+
+A key concept in calculus is the tangent line to a graph. Intuitively, the tangent line at a point on a graph of a function is the line that "best" approximates the function nearby that point. Using the concept of a limit allows tangent lines and their slopes to be rigorously defined. That the tangent line approximates the function near a point will be exploited in different ways.

quarto/differentiable_vector_calculus.qmd

@@ -0,0 +1,3 @@
+# Differential vector calculus
+
+This section discussions generalizations of the derivative to functions which have more than one input and/or one output.

quarto/integral_vector_calculus.qmd

@@ -0,0 +1,3 @@
+# Integral vector calculus
+
+This section discussions generalizations of the integral to functions which have more than one input and/or one output.

quarto/integrals.qmd

@@ -0,0 +1,3 @@
+# Integrals
+
+Identifying the area under a curve between two values is an age-old problem. In this chapter we see that for many case the Fundamental Theorem of Calculus can be used to identify the area. When not applicable, we will see how such areas may be accurately estimated.

quarto/limits.qmd

@@ -0,0 +1,6 @@
+# Limits
+
+The concept of a limit is behind most all the concepts in Calculus.  A
+limit in mathematics is the value some function or sequence approaches
+as an input approaches some value. It will be seen that there are many
+different ways to define "approaches."

quarto/precalc.qmd

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+# Precalculus Concepts
+
+The mathematical topics in this chapter come from pre-calculus. However, much of the `Julia` usage needed for the rest of the notes are introduced.